Even if 100% of global elextricity generation was replaced with nuclear, that wouldn't be true. You'd have to also replace (for instance) 100% of transportation with nuclear. (And that's assuming that the infrastructure construction and maintenance costs of doing all that are carbon neutral, too, and that the reduced demand and price for fossil fuels resulting from that shift doesn't open up new uses that get you back into problems, which—absent aggressive regulation—youd naturally expect it would.) [55% reduction is CO2 is needed, electricity is 27%, transportation 28%.)
Or maybe you are thinking that the absence of nuclear safety regulation would result in enough accidents to reduce the growth of population and industry enough to solve climate change, which I guess is a valid thought, if an extreme example of glass-half-full thinking.
Yet would one consider mandatory seatbelts and stricter laws on driving under influence and so forth "paralyzing regulation"? You are talking about the other extreme with its polar opposite of not having any rules. But there evidently is a huge middle-ground where we can have regulation and not having people killed in large numbers.
Consequently, if we look at history most of these "freak outs" have in fact resulted in regulation that has saved lives. Eg the gun laws in UK. We as humans are very short-sighted in general and I think it's more of a rule rather than the exception, that we need these kinds of accidents to improve the regulation and the laws in place. Sometimes maybe to the extreme, but I think it's better to be too strict than too lax.