That's not true. Nuclear waste is so minimal in volume nuclear power plants can just sweep it under the carpet. Or more specifically, just store it on-site. Modern nuclear reactors can even use the waste of old reactors as fuel and reduce it by another 80% or so. Dealing with nuclear waste is really no big deal. At least for medium term storage.

Storing waste so you don't have to look after it for thousands of years is admittedly more difficult. Then again, future generations are always impacted by the choices we make today and I'm pretty sure the kids 300 years from now would rather deal with the cleanup of our nuclear waste than with the consequence of global warming.