Wouldn't the government owning the service be the ultimate impediment to new competition?
I'm not defending ISPs, but lets not too quickly throw them under the bus.
Also, your casual throw-away comment:
> Most services that lend themselves to a natural monopoly ... should be implemented as a publicly run infrastructure
Requires the government forcibly taking over quite a few large companies.
That's a weighty request, and would be exactly the opposite of what we should want to see in the world.