We know that the Sith orchestrated the Clone Wars, and in secret controlled both sides. Their ultimate goal was gaining power over the galaxy and destruction of Jedi Order. Yet, books like Darth Bane and Darth Plagueis (both part of Legends now) tell us the story where the Sith didn't want Republic to die, they just wanted to keep it weak and corrupt until the right time came for a takeover. To that end, they sabotaged many separatist movements, forcing them to reveal themselves prematurely.
My question is, what would happen if the Sith chose not to act politically (not to pursue the position of Senator and later Chancellor), or simply didn't exist?
I imagine Republic would still be weak, with no large central military. Entities like the Trade Federation, Banking Clan, Techno Union, etc. would exist and wield tremendous power, first financially, then politically and latter militarily. Corruption would be substantial, and also the desire on some systems to break off.
It is entirely possible that in certain moments large corporate entities would start to use their military strength against smaller systems like Naboo, even without the goading of the Sith. The Jedi would be forced to act, but this time without the help of the Clone Army. Could the Republic survive this without splitting up ?