Up to how many hours of battery capacity?

Nuclear is expensive because nuclear is defined as expensive.

The problem lies with the standard of As Low As Reasonably Achievable. If you had reasonably priced nuclear power you could add more safety. Thus you have to add more safety. Thus you no longer have reasonably priced nuclear power.

And, when it comes to power it's a totally wrong standard. You should not be looking to minimize individual technology risk, you should be looking to minimize total risk of competing technologies. Making your nuclear plant safer instead drives generation to natural gas (~10x as dangerous as nuclear, plus climate effects) and oil (~10x as dangerous as natural gas, even more climate effects.) Or even coal (~10x as dangerous as oil, even more climate effects plus nasty stuff going up the stack--including emitting more radiation than would be tolerated for a nuclear plant.)