Nuclear power also leaves behind waste that is hazardous for between 10.000 and 1.000.000 years ( https://en.m.wikipedia.org/wiki/Radioactive_waste ), i.e. has t be stored safely for that amount of time. Most countries using nuclear power haven't even found a site to store waste permanently (e. g. Germany), let alone figured out how to tell future generations to stay away.
At this point we HAVE some nuclear waste already. Safely storing nuclear waste is an extremely difficult problem, and one we have yet to fully solve.
But if I have X tons to store for 10k+ years, what's the marginal cost of increasing X by a factor of two, or ten, or a hundred? (And what sort of increase in X would we be looking at?)
If someone told me to figure out how to affordably and safely store five megatons of nuclear waste (rough number from a quick Google search), I'd spend a lot of time with lots of experts figuring something out. If partway through you came back and said "oops, make that ten megatons", I might say "oh snap, our current site/plan doesn't scale", but I feel like it's more likely that I'd say "well, the bulk of the solution scales just fine". (Maybe the site wouldn't scale and the political NIMBY part would have to be redone, though, which is not a small problem.)
But I don't know! The fact that we haven't figured out the problem means maybe we should put some effort into that, but we if we're going to scale up nuclear, we should probably do it soon. Probably twenty years ago or so.