True, but with the first game, the Keepers were supposed to open the Relay after receiving a signal. The Protheans disrupted that signal. The Catalyst should have been able to do all that directly. You're right that messing with the signal is functional the same as somehow blocking the Catalyst's control, but only the former happened.
Do we actually know that the Protheans only disrupted the Keeper signal? They never came back, what Vigil states is the plan before departure, so it is possible that they found the AI's interfaces (or whatever) and blocked them.
This would allow the presence of the AI from ME1 onward without disrupting the trilogy too much.
In which case a normal cycle would start with the AI find the the 'reapingconditions' to be true. It signals the keeper to open the Citadel relay and awakens the Reapers.
-Using the keepers seems nonsensical, if the AI can do it itself, but maybe the keepers are also used to carry out other related tasks, before the actual opening-
Because the of the Protheans intervention, the keeper signal as well as the AI's control are non-functional this time. So Sovereign (which now is just the backup, backup-plan) needs to dock with the station in order to activate the relay itself, and/or re-establish the intelligence's control and/or repair the Keeper signal.
Sovereign tries that in ME1 and is destroyed.
In ME3 there is an unspecified amount of time between the Reaper capture of the Citadel and the time 'the fleets arrive'. So theoretically a Reaper could have docked in that time, just as Sovereign did in ME1, and restored the original AI capabilities and/or Keeper signal/response.
This leaves the AI unable to act for most of the trilogy until the last end. Which is pretty much what we see.
Which fits better than "the AI could act, but didn't want to". And I guess we all agree that it doesn't make much sense to build a huge trap/relay/reaperbuilder/spacestation around an AI and leave the only thing to be controlled by said AI to be an elevator on some unused part of that station...(couldn't even play that funky elevator music!)
This still leaves many problems, but conceptually it fits better than the alternatives, imo.