Let's not forget, the Republic might claim to represent the Will of the People, but only if the people support the Republic. Your people signed some treaty 10,000 years ago submitting you to a foreign power, and now you want to rule yourselves? Tough luck, sucker, the freedom-loving Republic doesn't put up with any of that nonsense. You can check in any time you want, but you can never leave.
They essentially view themselves as the legitimate government of the entire galaxy, exactly like the Empire. If you're not in the Republic you're A) a criminal-run cesspit, B) too primitive for anyone to care about, or C) an enemy of the state. There is no truly independent, coequal ally of the Republic.