The costs are not really due to regulations. They are because the construction industry is not exactly known for quality.
We know how to design safe nuclear reactors. We just can't build them cost-effectively, because there is always some subsubsubsubcontractor that doesn't bother doing things by the book. Then an inspector notices that something is wrong and orders it dismantled and rebuilt. And this will be iterated until everyone manages to do the right thing at the same time.
This is a propaganda talking point from anti-nuclear activists that is misleading and/or false. There are several misleading or incorrect levers used to justify this statement. The first sleight of hand is looking at the cost of headline capacity of intermittent sources. The second sleight of hand is the assumption that our current (insane) energy market pricing structure is reasonable. There's also the significant caveat that intermittent generation will depend on backstopping by carbon-emitting sources like natural gas. Finally, even reducing "capacity factor" to a single number is garbage. The minimum production really matters, and for intermittent sources, the minimum is zero.
Which is all to say -- it is not clearly and obviously correct to say that nuclear generation is cost prohibitive, and repeating it as if it were is a signal of bad faith.
And it is not really about "cost" anyway. It all hinges on the willingness of people with access to capital to take a risk. That could be a bank, large company, government etc. Renewables has managed to do that convincingly. Nuclear less so. And there are many good reasons for that.
And this one may cheaper than what we are used to. What is the important part.
(I still think it won't compete with solar+batteries. It still needs valves, turbines, and moving generators. Those things used to be considered cheap, but are becoming incapable of competing nowadays.)
the cost is because of the never ending redtape and legislation around safety. every design is obsolete by the time it's built because there's a new regulation that must be observed - so we never achieved economies of scale.