I can't think of any outer solar system probe that wasn't powered by radioisotope thermal generators.
Apparently, when they did finally manage to convince Congress to fund New Horizons, they actually got TWO probes financed, but they couldn't make the second since they didn't have enough plutonium for a second RTG. Of course, that's far from the only fuel you can use; since you only need it radioactive rather than actually fissile, your choices are much broader than for proper reactors.
It would be fascinating if they DID launch a reactor, though, then they might be able to power a fancy electrical propulsion drive.
Beyond that, though, there's a lot of extra red tape to put hazardous materials on top of a rocket.
You are right of course, that paranoia is always a problem. It seems like every time they try to launch an RTG into space, protesters show up because nuclear is a bad word, and they are too misinformed to know the actual risks.
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I'm sure SOMEBODY has already been wanting to send another probe to Pluto, and other Kuiper belt objects (again, a second New Horizons was on the budget to go elsewhere, but wasn't build), but if they started working on a new probe today, I can't see the next flyby happening any sooner than 15-20 years from now since it takes several years to design and build a probe and the flight time alone is nearly a decade.