Yes, in the future that is quite possible, although so far apart from 1080p it has not happened. It is quite possible that at some time in the future, all HD signals will be HDCP protected. At that point, if you are not using HDMI, then you won't get ANY HD. But there's going to be a massive outcry if that happens, because it would make ALL component video connections useless for HD.
We've already seen the removal of component video connections from BluRay players under industry pressure. My guess is that the movie/TV industry might pressure suppliers of set-top boxes to do the same. That would mean older equipment would still provide HD over component, but there would be no real need to add HDCP to all the HD signals.
Personally I think the whole thing is just BS. When you consider the amount of money the industry has spent trying to design copy protection into the technology, and the costs to all of us, and it still does not stop it happening on a commercial scale. IMHO they would be better off spending the money going after the people who do this as a business.