I agree.
Another example would be power (electricity). In some states, you can choose to buy power from solar, renewable sources, etc. The underlying infrastructure is the same; but the offerings change.
In the case of Internet, the government basically would give you access to some NAP or exchange; to get onto the Internet, you would have to buy access from some provider. Providers could differentiate themselves by a variety of services: some offering total privacy; some offering caching services so you get your content faster; some offering DVR/cloud services; etc. etc.
It is time we started treating access to the Internet as a service provided by the municipality, like water, power, sewage, roads, etc.