Hutts, prior to the Empire anyway, seem rather politically powerful as well... Remember in E1 they refer to Tatooine as being in "Hutt Space", which I've inferred this (and the fact Republic Credits aren't accepted there) means the planet itself falls outside Republic jurisdiction. Likewise, didn't QGJ mention ANakin "falling through the cracks" due to being outside the Republic?
Flash forward to the Imperial era and one of the positives of the Empire is likely a crackdown on crime... Also expansion. "Hutt Space" by the time of the Imperial era is maybe all but gone... They have influence perhaps, and their criminal behaviors would enable them to continue having influence in some way shape or form, but the Empire seemingly has taken over Tatooine... At least according to EU.
Since the prequals though, I've envisioned the Hutts as kind of like just "another option" for people to live/survive in. The same as choosing to live in the Klingon Empire in Star Trek, rather than live in the Federation... And like the "Hutt Space", there are probably other areas controlled by other groups/political bodies that don't want involved with the Republic. Look how many powerful groups are sick of the Republic and want to leave even. It's a lot, and they're incredibly wealthy/powerful, even within the Republic.