When this kind of thing happens it is well to remember that the voice at the other end of your complaint/request/&c is a little cog in a very large machine and has no authority to more than you detailed as your experience. If you are dissatisfied with your call, do not fold up and creep away; instead, ask politely and firmly to speak to the supervisor, manager, or CEO, &.
You will then be connected to someone that has authority to dig in, help you, and answer your questions. In the rare occasions when this does not happen, then you climb higher up the company tree until you get to someone that can and does help you.
Explosions of anger, such as you use in your message to this public site will do nothing to help your situation, and could make the nicest of staff bristle at being spoken to in such language. Remember, the voice at the other end of the line has done you no harm. They are merely operating a company system that you seem not to have researched before signing up. Honey catches more flies than vinegar, and being civil and pleasant with those in the service line trying to assist you, do not deserve to be subjected to abuse any more than you do.
My experience with Cox, 5 years TV, 'Phone, and HS Modem, has been punctuated with some of the best customer service it has been my happy lot to experience in a very long lifetime.
If, as you say, " ... when "high-speed" internet is working the tvs work crystal clear, " then why not leave your Internet connection 'open' all the time. that's what a cable modem is for, and it costs nothing to do so on top of your monthly payment, besides which, you say, it solves your problem of fuzzy TV?