Nuclear waste is really not an issue. You can literally glass it and dump it on the abyssal plain and it'll do much less damage there than the fossil fuels leaked from ships does.
(Yes, this is unintuitive. It's also true. The ocean is huge, the abyss not very active and water is great at blocking radiation.)
Because it's a complete nonstarter with the public (thanks to all the fiction like the Simpsons, Godzilla, etc) and the attack ads write themselves. Telling the public that they've been horribly mislead by their entertainment requires burning a LOT of money and political capital and isn't really worth it for any given politician.
Step 1 would basically be instilling Joe Q Public with an appreciation for quantification and if you can do THAT you've also solved a huge range of problems unrelated to nuclear power at the same time. This is also an _extremely_ difficult step that I'd expect to cost tens to hundreds of billions of dollars in education and propaganda.
There is a big erosion difference between glass dumped at beach with wave action and 10,000 feet down. Parts of the ocean floor are 200 million years old.
(Yes, this is unintuitive. It's also true. The ocean is huge, the abyss not very active and water is great at blocking radiation.)