I'm not sure if you're separating Legion from the rest of the Geth and the heretics, but I would disagree with this with regard to Legion. He does feel. On Rannoch he asks if the Geth deserve death. He doesn't ask if they deserve to be shut down or erased from existence. His question is based on the premise that he is alive, and, by virtue of uploading the Reaper code, the rest of the Geth will be alive. He then asks if Tali remembers the question that caused the uprising, likely in an attempt to make her feel guilt, or at least in the hope that she will understand his perspective. He then says that they "regret the deaths of the creators" while uploading the code. Regret is a feeling. He then experiences sadness that he will have to die to be successful.
I agree with the rest of your argument however, I'd like to better understand what you think specifically about Legion.
I'm not seperating it (the platform is genderless) from the rest of the geth because it is an instrument of and extension of their objectives even if it operates independently as a network within the network. I categorically disagree with the statement that it feels as well, as it shows no evidence of this. It is in essence a collection of 1,183 programs installed in an infiltraton and propaganda platform, designed to facilitate communication with (and the influencining of) certain organics in concert with geth objectives. The simulated emotional responses and metaphysical diction are no different than the synthesized voice's inflection or the nonstructural movable flaps on its head that simulate facial expressions. They serve no function in and of themselves, and are all designed with the platform's function in mind, enabling organics to more easily relate to it and assist in advancing the geth cause. It is tasked to coerce Commander Shepard and Co. into a belief in the superiority of the geth, and everything about it is a means to that end. In my opinion, it is quite an insidious, if brilliant (as clearly some of the people in Shepard's team and potentially Shepard themself are convinced by it, and the quarians it can come into contact with don't deactivate it on site) creation.
The geth don't actually feel those things. They are physically incapable of such. The "regret" line is likely targeted at improving Shepard's morale for the purpose of optimal functionality via simulated empathy after the latter is saddled with the responsibility of commiting genocide. If they didn't want the quarians to become extinct as a species, they wouldn't target unarmed civilian noncombatants and to the best of their ability wipe them out to the last man, woman, child and geriactric as they do or attempt to do in both wars.
The morality of the the Geth-Quarian conflict is completely irrelevant. Your job is to destroy the reapers by creating the most militarily powerful alliance powerful (measured in war asset strength) with everything else being secondary to that goal. The geth are far more militarily powerful than the quarians, who by all in game accounts are fairly poor soldiers and even more poor strategists and tacticians. The geth on the other hand, with the reaper upgrades, are probably the most powerful non-reaper force in the galaxy. To choose the quarians over the geth is both naive and a strategically inept decision.
Just look at mass effect 2. Legion is not only the most powerful squadmate in the game when fully upgraded, but he effectively replaces tali when you aquire him as he has the same default powers yet has twice the firepower and more than twice the durability ( with geth shield upgrades+geth shield boost).
Obviously the best choice is to make peace between them and get both to join the fight against the reapers, but if you have to pick one the geth are the better choice for fairly obvious reasons.
C'mon Colonel Radec you can do better than this. You are correct in your assertion that the morality is ultimately secondary to the short term goal of winning the Reaper War, but you are far off base with the rest of it. The geth are not "far more militarily powerful" than the quarians, at least not by the initiation of the Rannoch Arc. A massive portion oof the consensus is destroyed with their Dyson sphere in the quarian offensive, as is much of their fleet including seemingly all but one of their dreadnoughts (which is destroyed in the first mission of said arc). I don't know what "accounts" you are using to label the quarians as poor soldiers and tacticians, as on the former the only named ones we know (Kal'Reegar and his commando teams and Tali'Zorah) are highly effective soldiers individually, and they have to be because the quarians have a small population. Albiet, the quarians don't have anywhere close to as large a ground force as the geth (and this is correctly reflected in the War Assets) nor the ability to sustain one (due to the logistics of maintaining medical supplies), but the one they do have is more a precision than a blunt instrument like the geth or krogan hordes. They have differing uses, but "poor soldiers" is not a very good assessment when on Haestrom we see mere quarian squads of 12 Marines trading blows with entire geth platoons (Reegar's word, though in counting the number of geth on Haestrom they're closer to company or even battalion strength) and not doing too shabbily in holding out for significant periods of time against forces that are vastly superior numerically and further have armor and airpower advantages that the quarians lack.
Quarian strategic and tactical ability (especially in space combat) is commented on as being exceptional in more than one instance in game. The description of the Fleet in ME3 for instance
"A flotilla of 50,000 craft holding over 17 million quarians, the Migrant Fleet is the largest array of spacefaring vessels in the known galaxy. It is a testament to the quarians' strategic skill that these numbers have not dropped significantly during recent battle"
As does the Reaper war codex should you choose to disallow the code upgrade, with the quarians defeating a numerically far superior enemy force with "very few casualties" (according to Shepard).
"After the quarians eliminated the Reaper, the geth's processing power dropped precipitously and their bandwidth became clogged with queries for new instructions. Quarian fighters reported the exact positions of geth ships so that the liveships could fire safely on the geth from the far side of Tikkun, using the star's gravity as a slingshot. The geth command-and-control network was now in tatters, their forces separated by vast distances. The quarians hunted them like animals. It was not a one-sided victory -- despite vast losses, the geth staged a tireless defense -- but it was final."
The interview with Allers also has Shepard specifically denoting their prodigious strategic and tactical abilities should you side with them (which grants war assets by improving the morale of Gerrel's heavy fleet to its maximum of 280), as does Hackett when asked. I can't find videos on youtube of these though (probably because the Allers interview only talks about geth even if you broker a ceasefire, and killing them off entirely is unpopular). Zaal'Koris's and Daro'Xen's leadership abilities provide tangible assets to the war effort as well.
Further, the War Assets scores actually contradict you directly. The quarians can provide a maximum of 875, the geth only 815. Neither is likely "the most powerful non Reaper force in the galaxy". The quarian population is too small and the geth are vastly depleted by the war with the former. The turians hold that claim according to most dialouge in game, though this isn't reflected in the assets because unlike the quarians, krogan and geth (factions with higher maximum assets), their homeworld is directly under siege and most of their forces not availiable to assist in the Sword and Hammer forces.
Your assessment of Legion's gameplay ability is also not very good. It's a pretty mid tier squadmate in ME2. It's power set offensively is not very good against non synthetic enemies, with Hacking being entirely useless and drone being situational due to its ridiculous cooldown on squadmates. Comparing it to Tali as you did(who shares two of the same powers) it has a stronger anti armor but weaker anti shield/ barrier weapon in the Widow vs GPS and slightly faster cooldowns on drone and hacking, but lacks the ability to strip enemy shields over a wide area, which is a highly useful ability on insanity vs most factions (Collectors and Blood Pack excluded) due to every enemy having a protection layer. Geth Shield boost isn't particularly good even if you take 4 ranks of it for the weapon damage bonus, unless you are slow at killing and need tanky squadmates, in which case Grunt is still superior. In any case, Tali's pretty tanky on her own given a faction that can replenish her shields (which happens automatically while doing damage to the enemy), given the ability to double them up to a maximum of 600+ every 12 seconds. I never have problems with either of them being downed, and I never use Legion's boost over drone or hacking under any circumtance except when its AI decides to derp right up to the enemy. Overall, both are about mid tier and anti synthetic specialists in general. They are nowhere near as powerful or versatile as Kasumi or Miranda, for example. Garrus can also do most of the things that Legion does better, given his similar weapon damage but a far more useful and versatile powerset in area overload (which he has great damage and recharge passives for) and concussive shot.
In terms of what is the best choice from a strategic perspective, yes acquiring both forces gains the best outcome in the Reaper War, objectively and unquestionably once metagaming knowledge is factored in. If you have to pick one though, the quarians have more utility tactically, strategically, logistically and scientifically (Xen's research and individual skills provide up to 70 assets, compared to 0 from the geth), integrate into your current forces much more easily due to familiarity, and entail far less unnecessary risk both short and long term. The only tangible advantage geth have are numerically much larger ground forces, which aren't particularly relevant by this stage of the conflict (especially if you recruited the krogan for the same purpose), or as useful in general against Reapers as ships and fighters are.
If you re-write the heretics (which you should as there's no strategically logical reason to destory them) then the geth give you more, 825 IIRC while the quarians give you max 500, IIRC.
"No strategically logical reason?" Interesting, considering even the supposedly 100% logical mouthpiece of the geth consensus itself Legion will state rewrite as inferior and destruction as a "sound" decision should you ask it in ME3. The tactical outcome is potentially analougous (due to numerically equal 300 "unit" swings for both decisions), but rewrite makes achieving the optimal outcome (ceasefire) much more difficult, and long term results in more losses on the side where they cannot be replaced (quarians) due to the differing existential natures of organics and synthetics. Since the geth's primary unique utility as opposed to the quarians is their massive ground forces, and rewrite depletes none of their capability in that, I think you'd have a hard time arguing that there is any tangible benefit to rewrite.