For some people, their tolerance for bullshit is less than others. For those people, perhaps charging a dollar extra for YouTube access is enough. It only takes a fairly small percentage of customers to put a lot of pressure on service providers. Monopoly or not.
What you're describing is a substitute good. When the "choice" is to not purchase said product/service and look to alternatives, you're literally describing the effect of a monopoly.
My point is simply that a monopoly isn't some sort of God-emperor who can do anything without consequence. Even monopolies have to bow to customer pressure, they're just less sensitive to it than companies in more competitive industries. Supply and demand applies to monopolies, too, that's why their prices might be higher than they would be in a competitive environment, but their prices aren't infinite. "Going without" is always a choice, even if there are no competitors.
You can always put money on the lottery several times, win, buy your own satellite and have your own DTH service. Or kill yourself, so that you no longer need internet.
So no, there isn't always a choice in broadband service. And most times, there isn't a choice at all.