Demo downloads would get ridiculously huge, but I actually like the sound of this. We'd be able to play larger, more significant portions of games for a longer period of time before deciding whether or not to buy them, and slowly disabling or degrading features would be the incentive to buy.
Imagine a GTA demo where the entire map is opened up to explore, then after a week or something sections start getting closed off. I don't think this is stupid at all, especially if there's some sort of saving option where progress made in the demo can carry over to the retail/unlocked copy.