You said it yourself, nuclear is bad for the private sector as they can't rake the same returns as dirtier technologies. So why shouldn't we just let the public government do it? The U.S. Navy has more nuclear reactor experience than any entity in the world.
Yes, if you like communism then it is feasable to give away nuclear energy "for free". In the free market nuclear does not have a chance.
The military has specilized needs and is mainly interested in nuclear wheapons. Using the infrastucture to generate power is more or less a free "waste product" of maintaining that infrastructure.