As for the waste, that is a problem, and it’s entirely solvable. Much easier to solve than raging forest fires and the growing inhospitablity of climate change.
Compared to runaway global warming, even widespread radiation poisoning seems trivial. And such poisoning is both hypothetical and extremely unlikely to be widespread.
We need a change in a number of habits. We need actual leadership, and not only gov types. Etc.
Nukes are the easy short term way out. The issue is what that means over the long term and how it impacts the other vectors in entity. of this problem.
Without a wake up call we'll continue to mindlessly zombie on, as we have been. Nukes __might__ slow that (but only if they don't also create a false sense of overconfidence). However, they're not going to alter the course. They alone are not going to change the end.
Australia has long debated taking the world's nuclear waste, numerous commissions have found it feasible and safe. The community is overwhelmingly against it though.
Another consequence is that these reactors can use most of our existing stockpile of nuclear waste as fuel. It's the only technology that can actually reduce our waste stockpile instead of just storing it somewhere.
Storage for 300 years is generally considered a solved problem. I think the basic idea is to encase the waste in blocks of glass and bury them somewhere.
[1] https://en.wikipedia.org/wiki/Onkalo_spent_nuclear_fuel_repo...
Shortage? No. But energy could always be cheaper.