That's not true. I can easily imagine a world where there's a company which lays the cable, and charges any company who wants to use the cable a flat fee per month, or per unit of data, etc. As you said yourself, there is one provider who is fast, and one who is low, and the quality of service sucks in both cases much of the time. If that's the case, there are MANY customers in the area who are looking for fast, reliable, cheap internet, and there would be someone to provide it. If people don't want to invest or build their own miles of cables, they can lease it monthly from the company who specializes in that, and does it more efficiently than anyone else.
They'd be doing it already if the government didn't mandate regional monopolies to the cable companies who provide these services. The guy across the street from me can get FiOS, and I can't. It would cost next to nothing to run the line, but Verizon's not allowed to, so I'm stock with what I got, Net Neutrality or not. That's the real reason for the lack of competition and improvement. I'm stuck giving money to a company that isn't as good, because they're protected by a legal monopoly, when I would be giving it to the better company if they were allowed to grow.
Stagnant companies don't ever last in an actual free market.