A nuclear fission power plant is never going to be cheaper than a coal plant, and coal plants are very expensive. They're superficially similar types of plants: they heat water and then use a steam turbine to convert it to electricity. Coal plants use higher temperatures and pressures, so they can use smaller turbines. That turbine is a massive part of the cost.
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.
It can be cheaper to run a nuclear plant than a conventional power plant, due to lower fuel costs. But what kills nuclear is the capital costs of building the plant. It takes a while to reap the reward