I was young when the breakup happened but I certainly remember it's fall out. I have no idea why you think the government would need to set rates just because it forced the separation of the various corporate divisions. In most civilized areas that's known as a straw man argument.
If internet services and cable access services where separate there's no reason to believe a new monopoly would form. Much like dial up before you would be able to pick any ISP you wanted for your internet needs. Local monopolies for cable providers would likely continue because of the nature of the municipal agreements in place but internet service would have no such restrictions. In fact it would be nearly impossible to impose such a restriction. It would be like your town telling you what VPN provider you must use.
Beyond that not everyone is lucky enough to live somewhere like you. In my area (We would consider 20,000 a largish city) we have exactly one cable company (spectrum formerly TWC) and a phone company that couldn't offer reliable DSL if their lives depended on it. We have no competition, we have no choices. We pay top dollar for bottom of the barrel service. If I cancel my cable service and keep my internet it would actually make my bill higher.
What we do have is a local company trying to roll out fiber to home one town over (An ex dialup turned business provider). Because of the anti competitive nature of the cable industry they are being blocked, bullied, and sued at every turn. How dare they offer people a service they want!