You're misreading the claim. It's not that they have not given any approvals, it's that those reactors did not go on to reach operating status. That means these are more likely to be business problems, not regulator problems.
I don't think it makes sense to talk about the business of building nuclear reactors as something separate from regulator problems. The two are very tightly intertwined.
Four AP1000s are operating in China right now, demonstrating that under different regulatory regimes, the plants can be built.
I don’t see that as a useful question at all. The fact that China has working AP1000 reactors is one piece of circumstantial evidence that regulatory regime has an effect on the ability to build nuclear reactors in a timely way.
If you think that the regulatory regime plays a role, then there are three obvious questions to ask:
(1) is our current regulatory regime Pareto optimal on a safety versus build time plot? I.e. are there changes that we could make which improve build time without negatively affecting safety?
(2) should we consider moves along the Pareto front? I.e. should we trade some safety for some construction speed? Or vice versa?
(3) are there things that we can learn from other regulatory approaches that would help us address question 1 or 2? Your proposed question fits under here, but it should be much broader than the way you posed it.