I stand corrected on the 'power/mechanism' point, it's been a while since I've played the game now.
I'd still use the same argument though - the Citadel was the means by which to amplify the Crucible's already massive power - find another method for amplification. Or find a way to circumvent the Catalyst's role in the use of the Citadel.
The Catalyt's belief that the plan had been eradicated was conveniently naive - presumably it thought that the plans had been eradicated in previous cycles too. Certainly alarm bells should have rung when it became clear to the vanguard that they were losing the ability to take the Citadel at the beginning of the next cycle. Purely from a logical POV, if you know that there were plans out there that could build a weapon to stop you in your tracks the moment you set foot in the galaxy, they just required the use of the Citadel, which you no longer have access to, then your first step upon entering the galaxy would surely have been to take the Citadel as quickly as possible. Especially considering that the alliance had already proven capable of defending it to a limited degree.
Re the Protheans - the Reapers became aware of the device when certain factions amongst the Protheans were indoctrinated. At this point it would have become clear that any belief that the plans had previously been eradicated were wrong, therefore they were also prone to being wrong in any attempt to eradicate them ahead of future cycles. Equally, when Saren discovers that some Protheans survived on Ilos after the previous cycle, Protheans who were knowledgable enough to recognise the Citadel trap, surely there's at least a consideration here of "what else might they have done before they died out?" - hidden plans about the death machine that requires use of the Citadel, which they no longer have access to? For all intents and purposes, had the plans been discovered earlier then they could literally have built the Crucible right next to the Citadel and waited for the Reapers to enter the galaxy - granted, they wouldn't know that they'd be confronted by the Catalyst when they tried, but realistically, how would that have gone anyway? It apparently puts its hands in the air when Shepard confronts it at the end of ME3 anyway, even when it could seemingly win easily. Just by letting Shepard die. The reason for the Catalyst coming to the conclusion that its "solution" no longer worked was only a natural extension of what the previous cycles had been building towards. Even then though, I'm not sure how it comes to the conclusion that it won't work anymore - finish this cycle, sabotage the plans, re-establish the link between the Citadel and dark space, then nap time.