Yes, the logic is dodgy (tolerable is debatable) So my question is: Why does the dodgy logic only get used to screw the player?
This tolerable dodgy logic provided the setting for a game. However you perceive the ending now, the dodgy logic you're suggesting would make the universe look far worse.
They didn't because they were dependent on them. Just as the Reapers desired.
So? It's a commonplace technology that this civilization has harnessed. If it were that simple, they'd tear 'em down.
You don't think figuring out how the destructive capabilities are supposed to be unleashed might not be an important detail? I'd put it right up there with "how do I point this thing?"
It's less important when you trust the source and don't have any alternative, and the galaxy has gone above and beyond trusting the Protheans.
How on Earth did I ever beat Sun Li? or Jon Irenicus? Or, heck any enemy who's supposed to be older and wiser than the protagonist?
You really need to stop limiting the Reapers to "one enemy".
And the Reapers are faaaaaaaar older and seasoned than you're trying to make them out to be, too.
Except, you know, we don't really use the technology so much as blindly construct it and attach it without knowing how it works, or what it's supposed to do, or even how to properly build an "on" switch.
We have a general idea of how it works and what it's supposed to do. We just don't have specifics, and we're too desperate to abandon a ray of hope.
but hey, we can follow blueprints if we put enough effort into it. So go Team Current Cycle! 
Sure can, and they've gotta be kosher if the Protheans devised them. The rest of the galaxy still operates under the assumption that the Protheans built the relays; we know that they had a deeper understanding of the relays and other technologies like the beacons. Between those two sides, it's safe to say that they're a reliable source.
the unconventional attack was using one-man fighters against the thing in the first place. They didn't expect such tiny gnats to be flung at them, and exploited a potential weakness.
Uh, you mean except for the trained squadrons who quickly responded to the attack, right? The ones who nearly wiped out the counter-offensive?
Why on earth is using standard, coordinated fighters and a map to a strategic destination an "unconventional attack"?
But the point is using creativity and the tools you have to solve your problems. Not blindly follow in the footsteps of people whom "you would not know, and there is no time to explain" because, hey, we urinated away whatever lead time we had, and the writers went and built these enemies to be overly OP.
They've been sky-darkening enemies who wipe out advanced civilizations since ME1, and it took an enormous amount of effort (including a DEM datafile and a mystical connection to hopper Saren) to take even one out in ME1. They've always been "OP".
I'd rather have the creative, layered communication between previous civilizations that led to the Crucible than a true last-minute solution that makes all of 'em look like neanderthals, when if anything we're the "primitives" in comparison.