That's a major oversimplification. The reason the US is mostly (entirely) running Gen 2 reactors is because we simply lost interest in building new reactors for a long time. There were regulatory hurdles that caused this, but there were tons and tons of other factors that were (IMO) more important. Especially economic factors related to the cost and mismanagement of large nuclear projects, public opinions shifting over nuclear power, and alternatives like natural gas being super cheap.
The NRC has been approving Gen 3 designs for a while now but nobody wanted to follow through on building them.
Are costs and mismanagement directly related to regulations? Genuine question. This is impression I get from nuclear advocates like Mark Nelson and doomberg.
Yeah that's the complicated part. The regs are responsible for some of the mess, but far from all. It's a complicated subject, probably too much to get into here but you can look at the history of Vogtle as a start. Blaming the NRC is justified at parts, but it really only tells part of the story.
The NRC has been approving Gen 3 designs for a while now but nobody wanted to follow through on building them.