Carbon reduction is a global challenge, hence reengineered power generation is too. Normalizing nuclear means deploying plants in potentially under-developed or faltering societies around the world. While "London-sized" mistakes are increasingly less likely with newer technologies, the potential dirty-bomb weaponization of the fuel remains troubling.

The unforeseen consequences of nuke plants in places like Syria, Somalia, Lebanon, et al seem pretty bad.

(disclosure: I am a proponent of nuclear power overall)

Argument that hasn't been mentioned: Even though nuclear weapons and nuclear energy are different technologies they are still sufficiently close that betting on nuclear energy will probably diffuse more know-how on how to build nuclear weapons.

Sabine Hossenfelder's assessment (quickly) summarized (and possibly somewhat distorted by that):

• Uranium 235 is currently used at about 60K tons per year. World reserves are estimated to be 8M tons. Increasing the number of NPPs of current designs by a factor of ~10 means it's about 15-20 years until it'd no longer be economically viable to mine U235. Combined with the time scales & costs of building & mothballing NPPs, that's pretty useless. So while some new constructions might make sense, it's not good as a central pillar of a strategy.
• Due to the cost of NPP construction etc., nuclear power is way more expensive than all other options. Price of renewables is likely to continue to fall, widening the gap even further. So nuclear is economically very unappealing, and that's most likely just getting worse with time.
• Research into new tech takes time (e.g. designs that could use the other 99.3% of available Uranium that's not U235), and the currently available or soon-to-be available candidates aren't looking much better, they're unreliable and/or likely cost even more (at least initially).

As a supporter of the claim, 'in the long run, more nuclear power generation is a good thing', my best argument for why to not build nuclear power plants now is that I think we'd be better of first investing (a lot!) in more research on safety, reliability, efficiency. Commit to building beginning in 10 years after spending about 2 trillion dollars a year for those 10 years on research.

Nuclear power plants need to be a pretty specific distance from water, which hurts their use as a solution to a problem that causes rising water levels

Economics of nuclear reactors aren't particularly great due to regulatory costs and (at least in most western countries) low build rates/talent shortage. This can be improved by massively scaling nuclear energy up (including training more talent), but there isn't any political will to do that

Nuclear power has the highest chance of The People suddenly demanding it be turned off twenty years later for no good reason. Baseload shouldn't be hostage to popular whim.

I read somewhere about the higher risks related to cooling the power plant because of the increasing commonness of droughts. Not sure of the magnitude of the problem but considering the worsening climate for the next 30 years it does seem to be in good faith.

They may not be completely  passively safe?