There, I turned your statement around to show you how flawed your reasoning is:

The internet is a shared infrastructure, just like roads. As such it is serving a common purpose, and doesn't have to make money by itself (rather indirectly through enabling business). That's exactly where the government should be involved in. E.g. It makes more sense to have a single provider rather than several competing ones, providers shouldn't go bancrupt and be closed, and establishing them might require changing laws or evicting/relocating 1000s of people. These are all in the sphere of public responsibility.

Absolutely there should be competition, it's the main driver behind efficiency and quality!