You are right that on average, nuclear is safe and has a low environmental impact. One problem with nuclear is, that serious accidents can make whole regions uninhabitable for hundreds of years, if they happen. The probablility of accidents is low, but the dimension of accidents can be enormous.
What you also have to consider with nuclear is that keeping existing plants running generates very cheap electricity, but building new ones does not - in fact, it is amongst the most expensive options available for new builds. Only residential rooftop solar can be more expensive under some circumstances [
1]. Seeing that the cost for PV keeps declining, that won't be true for much longer, though [
2]. Further, the total Uranium reserves known today are only good for just below 100 years if consumption stays at current levels [
3]. You can assume that new deposits may be found and they typically are, but the reserves are limited and if you increase consumption now by building new reactors at scale, the reserves can quickly come down to a couple of decades.
Therefore, keeping existing plants running, keeping them safe and upgrading them to some extent is a reasonable choice. Building new ones now is debatable. Relying on nuclear in the long term (50+ years) isn't even a choice. Other solutions are required for base load applications. The only viable solutions for that are large scale storage + renewables or - if we ever get that running - fusion power.