US doesn’t do it because the highly-radioactive byproducts generated by the reactors were at one point the desired end-product. But even so, it’s a miniscule amount — such that things like “having an off-site storage facility” are problems that have been put off for decades (and probably can be for a few more).
In the US the Carter administration stopped spent fuel recycling due to it's fears of nuclear proliferation. Didn't make sense to me at the time and still doesn't.