Have you seen the Netflix streaming catalog? It's terrible. People would pay substantially more than that just for current episodes of the HBO original series, to say nothing of the movies -- which they already do pay for the cable package. Why do you suspect they wouldn't do the same over the internet if the choice was available? Once again, they would likely pay even more, because they could then more easily cancel their entire cable subscription while paying HBO more than HBO is currently receiving today from the cable companies and come out ahead.

The primary problem is that HBO would have to transition their subscribers to their internet service all at once or they would lose subscriptions. There are still plenty of HBO subscribers watching on analog TVs with no internet attached to them, and HBO can't take steps to make itself independent from the cable companies without causing them to retaliate by depriving it of all that subscription revenue.