There are any problems with fission that are all related to the extraordinary danger of handling the fuel, byproducts, and the sites themselves.
The cost of them is huge, some people are hoping that modularity will help with construction, but it is still astonishingly expensive.
The problems of handling the fuel has been solved, in theory and practise. Except when commerce is involved. When the money people get involved corners will get cut, and we are back to incredible danger. Technically solvable, but I would not go near it. I have known too many business people.
The problem of the long-term waste is entirely beyond us. There has been no practical progress on this front. Long term waste (including some parts of the assemblies themselves) are very dangerous for hundreds of thousands of years.
This is, with current technology that can be bought to bear, unsolvable.
The only thing we can do is put it in a stable site, be ready to move it when the site becomes unstable (nowhere on Earth is known to be stable on such time scales), and find a way of communication, across thousands of generations, just how poisonous this stuff is.
Maybe our ancestors will get lucky and find a way to safely dispose of it....
So fission power is making future generations pay for today's consumption.
Fortunately for us it is moot. The costs of renewables is dropped to the point that the only reason for fission is to build the capacity for nuclear weapons.
If fact more people die from falling off wind turbines during maintenance than have died from nuclear accidents on a per-TWh basis [1].
And there were greater health effects in Fukushima due to panic and unnecessary evacuation than from radiation [2].
Again I agree radioactivity = bad, but I think it needs to be put in context.
And as for the disposal of nuclear waste, yes it's a problem for thousands of years, but we don't need a thousand year solution, it's not like we're leaving the planet. One possible outcome there is that eventually we develop cheap enough neutron sources that we can bombard the waste with neutrons until the various atoms capture enough neutrons to become stable isotopes. Considering the technological progress over the last 300 years, maybe in another 300 such a feat will be economically feasible.
reprocess the dirty fuel and bury the actual waste deep underground like Finland is doing at the Onkalo spent nuclear fuel repository.
https://en.wikipedia.org/wiki/Onkalo_spent_nuclear_fuel_repo...
And there is still very much a need for zero-carbon DISPATCHABLE electricity of witch nuclear is the ONLY choice. You simply cannot have 100% of your electricity from only solar and wind because it is far too variable and we simply don't have the technology to store electricity cheaply enough.
Your attitude towards nuclear energy is as irrational as the average antivaxer towards vaccines.
How deep, to stay put thousands of generations?