I don´t think they could have made Wrex a trilogy squad-mate. Not that he does not deserve it, but because of the way ME1 was designed. You may play the game entirely and just briefly run into him. Not to mention that he could potentially be dead.
With the exception of Garrus, all characters that could potentially be dead by the end of ME2 (including the virmire survivor) have very diminished roles in ME3. When we consider that both Wrex and Zaed are bounty hunters, they seem to be logical choices for squad-mates till the end of the series after being introduced. But then they decided to to re-work Wrex as being an optimistic leader who never gave up hope (a retcon, since in ME1 he very clearly gave up on the decadent krogan society and totally lost hope) and unites the clans, while Zaed was just standing on the citadel when he could be doing something like shooting reapers and cerberus.
Not to mention that jack may still be around while there are hundreds of cerberus troopers in need of dying.
Instead, we get a high-ranking military advisor and a quarian admiral (well, potentially, since she could also have been exiled) that can die from a cut in her dress but yet is a logical choice of squad-mate for you.
But they did have loyal and vocal fanbases, and the fact that they appeared both in ME1 and 2, becoming the only trilogy-squadmates.
I once did a trilogy run trying to use Garrus and Tali whenever possible (and doing all that I could to speed up their recruitments by delaying side-missions). I used a female biotic shepard in order to complete what both of them lacked. Tali in ME1 with a good omni tool and 2 medical complements to her suit (drastically reducing her cool-downs) can be a beast made of sugar. Together with Garrus they could easily incapacitate most targets along with my shepard´s stasis and singularity.
ME2 and 3 sucked because it took too long to recruit Tali, even though I speedrunned to recruit her (I only did the rachni side-mission so the priority missions could go on while still leaving me two aditional missions with the turians on the krogan planet).
But what have I done recently? Well, I´m now using John Shepard. The sheploo model, without modifications of any sort. And trying to do the most complete run from a story-perspective, taking with me the characters that will offer (in my opinion) the most expanded notion of each particular mission. Like having Zaed and Grunt while recruiting Garrus in ME2, Liara on Illos and Noveria, Jack at Miranda´s LM, Garrus on Horizon for the extra comment from the virmire survivor, Javik on Tessia, and so on...
I was quite surprised at how easily recruiting archangel turned out to be. Usually I have to take Miranda with me. She is great thanks to the increase in the team´s weapon damage, and her warp is useful against shields and barriers and her overload means instant-death followed by explosion on the pyros. But Zaed and Grunt both revealed themselves killing machines even without miranda´s support. Grunt only used assault rifles, switching to shotguns only during the close confrontation inside Archangel´s base when the krogans and vorcha invade. Zaed alternated between sniper and assault rifle the whole time. I thought it was going to be tough, since I could not trigger biotic explosions, but it turned out to be really easy in fact.
So I went to horizon, taking newly-recruited Garrus (for the extra-comment from kaidan) plus Mordin with me (Mordin has a different scene at the opening saying he needs to personally test the defense against the seeker-sworms).
John Shepard arrived at the normandy only to discover that Jacob is acting a little strangely with a cryptic tone, and that the mailbox has been flooded while he was away. It seems that quite a lot of people want suddenly to talk to him, from Admiral Hackett to Miranda Lawson.
Next, John will recruit Tali and the 2 remaining Illium companions prior to doing any loyalty missions (Zaed´s and Kasumi´s are the only ones already done).
This John Shepard doesn´t romance anyone aside from Kelly. And possibly the reporter at ME3.
Pretty soon he will eat his words from all the times he cursed the Mako in ME1. He will actually miss the vehicle when he goes against a geth colossus on foot. Let´s see if I can win without resorting to a heavy weapon. Should he survive, pretty soon he will be dining with Kelly.