You have not proven that these regs are unnecessary. And, in fact, there have been some close calls on serious safety issues (see here, for example). Even the nuclear industry won’t make the sort of claims that you are making here…They emphasize that regulations must evolve with technology and such but they won’t make the claim that the regulations currently go far beyond what is necessary (see their statement here).
Also, there has been a study comparing the costs of nuclear energy in France, Japan, and the U.S. and, like I noted before, the issue isn’t that nuclear costs more in the U.S. than these other countries but rather that the fossil fuel alternatives cost less.