What are these natural monopolies?
Dude cmon. Energy, water, rails... when I need to get the train to my Mother's, I have exactly one company to choose from. They can charge whatever they can get away with.

It is by the potential to make profit that resources are allocated to the thing in the first place.
The govenrment's profit comes from increaed tax revenue caused by a stimulated economy.

However, what happens to the trains when there is no profit to be had by making a better train good or train service to consumers and potential consumers?
There's always profit. Someone has to build the new trains, or refurb them, or provide the imroved service.