Also, do they really need the AI itself? It could've been not present and Shepard could still use the Crucible because it docked at the Citadel and disperses the energy via the arms. Shepard may not understand what's going on because no one explains it, but it would work without the AI I believe, since the Catalyst (and also Vendetta before) explicitly states that the Crucible in combination with the Citadel and the mass relays can release its energy. The AI is not really a part of this process, or is it? Correct me if I'm wrong or overlooked something.
Well we need the catalyst. The catalyst is according to the amoral AI, the amoral AI.
And "to do what" with the power was stated. Use it against Reapers of course 
Well, as we found out, what it´s used for, is actually a choice.
Yeah, but what's the problem with that? They use a core to replace another core. Whether they did test it to some extent, we don't know. I don't remember Hackett saying anything about it, but I will keep an eye out once I get there in my current run.
The advanced power relays are optional though. If you never side with Xen, you don't get them.
I took a (hopefully) funny stab at it a few posts above. Well the point was, you said we only added stuff at the periphery and nothing that affected its core function. Its core function is providing a huge amount of power (according to our friendly clippy app, the starkid). At this point you meddle in the core function.
And yet again, does it really make a difference how the Crucible does what it does and what the Catalyst tells you? Whether you know how it works, or believe the Catalyst's words or not doesn't matter, you still have to deal with the problem at hand, still have to disperse the energy somehow (ok, minus Refuse obviously), and that's why I say it's the most important part.
Well, if we want to make a meaningful choice we should perhaps know a bit more what we are actually doing and who exactly is presenting this choice and in what state of mind.
I thought it was clear we'd be in a situation like this, just like in the game 
Yes, silly that people expected something else. 