They can, if the public providers let them. It's a choice in that regard, since the government can simply say "we'll offer at 10% of our cost, and subsidize it

They can, if the public providers let them. It's a choice in that regard, since the government can simply say "we'll offer at 10% of our cost, and subsidize it with taxes", in which case you can't compete unless you're insanely more efficient than the public provider.