The US has been using order-of-magnitude the same amount of nuclear power since the 80s. This has been a non-issue for longer than most HN commentators have been alive.

If politicians ever decide it has become an issue, the storage facility can be constructed.

WIPP exists[0]. This is just for weapons waste (which is a much higher concern btw). But honestly storing waste material on site isn't that big of a deal. The DOE has also invented significantly better storage systems in the last 50 years but simulations and small scale testing do not count as proven enough for large scale testing ¯\_(ツ)_/¯

But there are other deep geological repositories around the world.[1]

[0] https://en.wikipedia.org/wiki/Waste_Isolation_Pilot_Plant

[1] https://en.wikipedia.org/wiki/Deep_geological_repository

What's more likely to kill us, nuclear waste or climate change?