There's always a choice. Suppose your ISP started charging you $10,000 per month for the service you have now? Would you pay it? Could you? No, you'd probably just go without home service, or rely on your cellular data plan, or get dialup, or just take an internet sabbatical until the ISP cleaned up their act.
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.
That's a poor way of trying to weasel out of the actual definition of monopoly, which is defined as "a company or group having exclusive control over a commodity or service"[0].
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.
I'm not trying to weasel out of anything. Of course they're monopolies.
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.
We're talking about reasonably priced broadband services, no need to be pedantic or literal.
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.