I've already noted that the accident rate is far more dependent on organisational rather than technological factors. As such it's less subject to progress, and that progress likely has flatter curves and lower intrinsic limits than technological processes, especially those similar to Moore's Law.
Automobile safety is a domain in which we've extensive experience, and what is shown is a decreasing trend in absolute numbers, as well as in percentage safety. In the first decade of widespread adoption in the US (1910--1920), the accident rate per passenger mile roughly halved. It's halved every two decades since, as contributions from a number of factors are combined. Some risks, notably toward pedestrians, have remained largely unchanged or increased over the same period.
In the power sector, the record from hyroelectric facilities across countries shows a similar trend, with early immature sectors exhibiting major disasters, which fall greatly by time. But the pattern itself repeats across countries, and there's some uptick in risk as aging and poorly-managed infrastructure either fails or experiences near-failure. See for example the Edenville and Sanford dam failures in Michigan in 2020, and the near-failure of the Oroville dam in California in 2017.
With more nuclear power plants, there'd also be more plants in more places, including in less well-governed or more unstable countries. Note that in Eastern Europe, the Balkans, much of the Middle East, Southeast Asia, South and Central America, and Africa, there've been numerous transitions of government, as well as coups and outright wars, often with major terrorist / partisan freedom-fighter components. We'd have to presume that these would have occurred with a much more substantial nuclear power component.
Under such conditions skilled engineering and management talent often prefers seeking better conditions (higher paying, more stable, safer) elsewher (brain drain), coption of programmes for non-generation purposes (explosive weapons, dirty bombs, other forms of coercion) is far more likely (see Iran and North Korea as two examples), nuclear proliferation, already widespread, would likely be much greater, a even simple errors such as siting on poorly-suited or improperly mitigated locations (as was the case at Fukushima-Diaichi) would be more likely.
Then there are the fuel preparation, delivery, and waste management issues, as well as site decomissioning needs.