The regulatory costs of nuclear are mostly occurred in the design phase. Those costs are sunk and mostly irrelevant for new builds of old designs.
The fact that old designs like the AP1000 are crazy expensive to build has a lot more to do with the fact that the US sucks at building mega projects than anything else.
Interestingly, one of the reasons the design phase for nuclear is so onerous is the sheer amount of red tape involved due to compliance and other regulatory reasons. You wanna know something funny? You know what's really good at generating piles of convincing sounding bullshit that it's possible no one even actually reads, and looks like it's totally going to insert fuel rods into the nuclear power industry?
Other countries are better at building particular types of mega projects. Some are better at transit, others are better at building tunnels, others are better at building massive ships, et cetera. But in regards to nuclear, I believe you're right.
I'm getting the impression the problem isn't any particular regulation, but rather than because regulations exist, the design is fixed.
Getting a design approved means a specific design is approved. So, the power plant must be built as designed, no changes. And apparently ensuring you built exactly what the design specifies is really expensive.
What's needed to reduce this cost is having some way to get a whole cloud of closely related designs approved, so that reasonable deviations from the design are also approved. This is equivalent to saying only the most critical part of the design would need to be built as designed, everything else would be allowed some slop. With something like this, one might (for example) be able to build the confinement building with less tight control on the configuration of the reinforcing steel.
I'm don't know how one would get such a cloud of designs approved. Maybe this is a problem that could be solved by massive computation? Run billions of mutant designs through a simulation gauntlet to see how sensitive it is to various perturbations? Or maybe add more defense in depth, like devices that scrub radioactive elements from steam (such things exist) so the tolerable chance of meltdown can be allowed to increase while keeping expected damage in check?
Sounds kind of like hyperparameter search - you're searching the design space for the bounds of the different parameters. I don't know if parametric design is possible on reactors, but would be neat if possible.
The fact that old designs like the AP1000 are crazy expensive to build has a lot more to do with the fact that the US sucks at building mega projects than anything else.