The Republic realistically wouldn't have lasted if the Force was removed. It would have broken apart into a very large number of pocket empires that all have effective planet destroying weapons and as a consequence you are going to end up with basically eternal, incredibly bloody, war.
The Jedi were the people who ended up in the right place at the right time to be able to defuse all of the little catalysts that would spiral out of control if not interfered with.
The Force basically means plot shields and that the galaxy bends itself to ensure that you are in the right place to accomplish your goals (whatever they happen to be). For the Jedi their goals were generally the good of the Republic, for the Sith it's usually galactic conquest or whatever.
That's your fanon, as far as I can tell. And that's fine, but to my knowledge, nothing canonical supports it. Maybe in Disney canon, if something like that has been suggested in the High Republic stuff-- I wouldn't know about that. But in the original continuity, there was no suggestion of this being the case.
Huge galaxy, 10.000 Jedi, meaning they're a very small group... and yes, they did good stuff. Guided by the Force, they were doing good. And at the same time, the Sith were undermining everything, and
starting conflicts and problems. Remove both, and what is left? Just human action. (Or in this case: sapient action.)
The Republic would, by all evidence, do just fine without the Jedi (provided the Sith are likewise gone). Remove the Force from the setting, and there's no reason (that we are ever shown) for the Republic to just crumble. It would have good times and bad times. There may be times that it falls apart, but by all evidence (in the old EU, at least) it just as reliably fell back together. And of course, while the heroic Jedi played a role in that most often... the depraved Sith typically were the ones to cause the problem in the first place.
This seems to support the potentium interpretation. The Force isn't keeping the Republic together. The Force just
is. And you decide how to wield it. Sapients being (as we are shown) reliably fallible, the results tend to even out. Some good, some bad. Overall, it really seems like the hypothetical absence of the Force wouldn't make things better
or worse. It would still just be a case of "people gonna people".