I think Sidious accelerated the collapse of the Republic but I don't quite believe that the Republic actually works, as Anakin mentions, they spend a lot of time bickering and nothing gets done. Same with the Rebel Council, same with the New Republic. All 3 situations it takes a strong move of someone outside the system, Sidious, Jyn and Cassian, and General Organa, to get things moving from the Republic senatorial stalemate. (Yes, I know I just compared Sidious to Jyn and Leia but kinda roll with it. he DID get things done, wicked and evil they may be.) There hasn't been much pre-Naboo Crisis content in canon yet but I'm pretty sure that Legends had a whole lot of Old Republic in crisis stuff that didn't have Sidious pulling the strings.