From Earth, it is much easier to eject something from the solar system than to get it to fall into the sun by the way.

Well, not just Earth but from almost everywhere in the solar system (assuming being on an almost circular orbit).

Too dangerous to send up in a rocket, especially considering we can reprocess and concentrate our nuclear waste into a absolutely tiny amount and bury it so far down that it will never reach the surface of the earth ever again. But of course without a large stable nuclear industry there is no demand/profit to be made from nuclear reprocessing when you can't get the materials to reprocess long term. We also have to deal with a bunch of old and outdated rules that give hard no's to certain reprocessing technology which was decided before we understood how most if it even worked.

As long as you're sure it'll actually go into space and not just explode in the upper atmosphere.

Given unlimited money, this might be reasonable, but it's worth noting that the delta-V requirements for shooting something into the Sun are pretty astronomically (pun intended) high.

Why not? Because the environmental cost of a failed launch is massive. It's radioactive roulette. Where it lands... Depends on which way the wind is blowing.

You people are atrocious pedants.