ByeBye Diesels

[nominous]

Nuclear propulsion allows a submarine to remain on operations without refuelling for huge lengths of time
Not using nuclear power to power a new submarine is designing it to be at a tactical disadvantage from the offset until someone comes up with something even better.

The germans and the scandis (and the ruskies) are all investing in diesel boats which can be quieter than equivalent nucs.
They dont have range, but they are capable of loitering just as well if not better since they can do that on batteries and fuel cells.
But a missile sub is about hiding the missiles. It's operational range doesn't need to be wide when the missile has a 7500mile radius of operation.
The point is that it's not a fat stationary target like a silo.
It could in somewhere in the north sea. It doesn't have to go far to be a strategic weapon/asset.
And for the price of one nuc you can have several diesels. Maintenance is cheaper naturally and you can have more boats cycling in/out of port to combat the lack of endurance.

A hunter killer as a nuc sure. If the task is patrolling the worlds oceans. But if it's coastal defense then again a diesel should be ok.
Going into Cold War II I'm sure having both types (missile and hunter) being nuc will be an advantage.
But it is a tremendous cost.

Issues with this solution? How to sterilise huge volumes of people especially outside the western world.

Give them something in return. Like money. No reason to limit it outside of the western world either.