That assumes there are enough people who care about quality of service over price to make a private alternative tenable. There is a reason why there is no private competition to municipal bus systems, even really terrible ones.
Sure there is competition for the municipal bus system - taxis and ride share services. It's almost the perfect metaphor. For those who want faster service they look for options that offer these things at a reasonable price, and for those who don't care about fast speeds or cannot otherwise afford or justify the cost use the lowest common denominator, which is the public provided system. However, with internet service, there is no fallback.
There are totally private competitors to the private bus system, and there is private health insurance in places like the UK with social healthcare. I understand your point but I can't think of a single industry that doesn't have a natural monopoly where there wouldn't be room for two competitors based on differentiating solely on price