Also, if you're serious about the problem of "our nuclear power plants are producing more power than we need and we can't turn them off because then we'll have

Also, if you're serious about the problem of "our nuclear power plants are producing more power than we need and we can't turn them off because then we'll have a power shortage", there are applications to dump "bonus" energy into. You'd run into the same problem with renewables too; the difference is that with nuclear, you can avoid the "not enough energy" problem.