The other thing about a half-life of 10,000 years is it means the actual radiation is very, very small. If it was large, it wouldn't last 10,000 years.

The way to make nuclear waste safe is not to concentrate it and bury it. It's to disperse it in such low concentrations that it doesn't make any difference.

That's too far the other way. Material that's safe in 10,000 years (which means the half-life is significantly less) is highly active and not something you want to hang out with unless it's shielded. The longer-lived stuff isn't all that great either when it gets inside you. Being near a bunch of uranium is fine, but breathing it in is considerably less fine.

Several countries tried your approach around the middle of the last century, pulverizing large amounts of radioactive material and dispersing it into the atmosphere. The results weren't catastrophic, but thousands did die from it.

We shouldn't be irrationally fearful of nuclear waste, but we shouldn't be completely blase about it either. The stuff is dangerous... just not dangerous on a level beyond anything else out there, the way many treat it.

There's also a considerable difference between the poisonous chemical properties of heavy metals, which will persist, and their radioactive danger.