We have a permanent, forever solution to nuclear waste, it's just that no one wants to pay for it. It's easier to just keep kicking the ball down than solve the issue permanently.
It's called deep borehole disposal - you drill a hole down to Earth's crust(~5km or deeper), fill the bottom 1-2km with nuclear waste, fill it back up. Literally solves the problem forever. It's not coming back up on anything shorter than a geological timescale, and the land above the borehole is perfectly safe to live on.
The main reasons why it wasn't and isn't pursued is
1) cost - drilling itself is "solved" but inventing new storage casks that would fit the hole and re-processing the waste to fit is a new engineering challenge which would cost money
2) the idea that nuclear fuel, even spent, can be reused - either in breeder reactors, or for other purposes. If you bury it 5km deep it's almost impossible to retrieve it.
https://en.wikipedia.org/wiki/Deep_borehole_disposal
The above is why I'm kinda annoyed when people say that nuclear is bad because we just produce waste that will pollute for centuries. Like, yes, but we also know what to do with it, we're just unwilling to pay for it.