We already have inherently safe nuclear reactors[1] that automatically power down if the core gets too hot due to the physical properties of the fuel, without the need for an electronic control system. However, incidents such as Chernobyl, Three Mile Island and Fukushima have already tarnished nuclear in the public view, making it politically unfeasible to spend money on new reactors. This is a good summary of the situation: https://www.technologyreview.com/s/602051/fail-safe-nuclear-...
It has to be said again that RBMKs like Chernobyl are a terribly unsafe design, in that they have a positive void coefficient and can go prompt-critical (basically the core can explode). If you read between the lines, this design won in the USSR because it was easier and cheaper to build[0]. The soviets also (allegedly) skimped on the construction[1].
Since way before Chernobyl, the US has been operating LWR and PWR designs, which have a negative void coefficient and therefore can be built to be passive-safe[2]. Correspondingly, no deaths have ever been directly attributed to failure of a production LWR or PWR.
It was, and at no point during that incident was there any plausible risk of the core going prompt-critical or radioactive fuel being thrown into the atmosphere. As I remember it, the most serious risk was that the earthquake or tsunami could have damaged both the primary containment and the concrete "bathtub", so molten core materials could have leaked into the surrounding terrain. That's why they pumped in seawater to try to keep the core from melting down (an attempt which did not succeed).
As far as I know the primary containment for all Fukushima reactors is still intact.
But I think your explanation sort of highlights why promises of "safe nuclear design", at least in my opinion, have a tendency to be overstated by nuclear proponents, and then result in a complete backlash against nuclear when things go wrong.
Fukushima was a Level 7 disaster, on par with Chernobyl, that will result in large swaths of Japan being uninhabitable for lifetimes. Trying to make a distinction that it wasn't really that bad only makes your average Joe discount any assurances that "passive safe" is safe at all.
> Fukushima was a Level 7 disaster, on par with Chernobyl
This is disinformation. It's an arbitrary bureaucratic designation (Level 7 means "measures were taken to mitigate effects"), and the two events were incredibly different.
> that will result in large swaths of Japan being uninhabitable for lifetimes.
This is completely false. I've said before that if it were legal for me to do so, I'd pack up and move to the Fukushima site tomorrow. I would never say the same thing about Pripyat.
>What’s more, the new plants should produce little waste and might even eat up existing nuclear waste.
>That means they should dramatically reduce the amount of nuclear waste that must be handled and stored.
But doesn't go into detail about exactly how much waste is generated, how waste is handled and where waste should be stored. This is exactly the problem with nuclear, and our ongoing battle with Chernobyl's corpse is exactly the worst manifestation of that problem.
Molten salt reactors have their issues too eg. "The primary concern with MSRs is that the radioactive fission products can get everywhere. They are not in fuel pins surrounded by cladding, but are just in a big, sealed vat." - https://whatisnuclear.com/reactors/msr.html#problems
No full scale ones, AFAIK. India and China are investigating the technology. Oak Ridge laboratories ran what was essentially a proof-of-concept MSR achieving criticality in 1965, operating until 1969. Lots of interesting history behind that, as well as interesting findings. They supposedly fuelled it with plutonium at one point...
That only solves some of the many failure modes. Much like preventing the Challenger disaster from happening again did not prevent Columbia from failing.
[1] https://en.wikipedia.org/wiki/Molten_salt_reactor