Yes, there's room to drive down the cost of nuclear. No, it's never going to be cost competitive with solar/wind/batteries, no matter how much you drive down the cost or eliminate regulations.
By unsolved I mean - not convincingly solved, and certainly not yet tested over the expected duration that material needs to be safely contained.
Even if the storage got somehow compromised(extremely unlikely), the disposal sites are distant enough from civilization and the amounts small enough that the environmental harms would still be far below tons of other manmade events.
What more do you want?
I'm not sure where you're getting cheap from, or low-maintenance.
The above-ground stuff is locking future generations in for on-going maintenance for several centuries, perhaps longer. There's been think-tanks trying to work out how you just signpost such a place, given storage may exceed the expected lifetime of languages, and we'd want to be polite and at least contend with societal collapse.
It is hubris to observe that the many locations chosen now will remain 'distant from civilisation' for many centuries.