Nuclear is very inexpensive once the plant is paid off.

That's a lie. The most expensive part of nuclear energy (which is also very CO2 intensive) is enrichment and waste management, at least in countries that don't have the freedom to dump it somewhere in the ground in the middle of a desert.

If you include all its costs that are today externalized to the tax payer, nuclear energy (at least in in Europe) costs way more than PV and a lot more than wind energy. (IIRC ~8ct/kWh for nuclear, ~2.5ct/kWh for PV, ~1.5ct/kWh for wind)

Basically nuclear is expensive because we don't build them often enough.

Scaling it just means more waste to deal with, so no, it wouldn't get significantly cheaper. Whatever you save in terms of scales of economy would have to be spent on dealing with the additional waste.

Also renewables may have less capital expenditures in construction, but their lifetime is also significantly less.

That's also a lie. Modern PV cells are expected to have a lifetime of 25-50 years, that's on par with fission reactors. The PV cells also don't radiate afterwards.