> Or just use reactor designs that have a negative void coefficient and won't end up in a positive feedback loop.
Positive feedback loop isn't needed for a nuclear accident to happen. Sure it's what happened in Chornobyl, but not in TMI or Fukushima. And from an engineering perspective Chornobyl isn't that interesting as an accident example because it's mostly a product of brainwashed egotic manager who had all the power over the engineers.
Also it's not always entirely straightforward to keep the void coefficient negative at every point of the operating cycle, especially if things go wrong: PWR have a negative void coefficient most of the time but not 100% of the time: when the reactor is cold you put tons of boric acid into the water to counteract the reactivity and avoid divergence, but at this particular time the void coefficient is positive because of the high level of Boron. Of course in regular events it doesn't matter because the reactor is off, but that's something that can also happen during an emergency situation where you inject a massive amount of boron in the water (there are scenarios where you do that).
But again, the reactor's power getting out of control isn't the biggest risk anyway, the biggest problem comes from the fact that residual power is still annoyingly high even when you've shut down your reactor and you need to deal with it. The fact that you can't just shut it down and everything's OK when something is wrong is the real pain of working with a nuclear reactor.
Source: I have a nuclear engineer specialized in immediate response to incidents and accidents at home.
And the high cost mostly comes out of the fact that we don't build nuclear reactors as series + the fact that we finance it at insane rates. Antinuclear activists have their responsibilities in that, but even without them I suspect most states wouldn't be doing the right thing either: nuclear isn't a good fit for neoliberal thinking anyway.