Your describing a scenario where people play all their games all the time, constantly changing between them. I don't think many people work that way at all. I think it's far more typical for someone to buy a game and play it until they've had enough, and then they buy a new game. In your example, after losing all your games, you'd only need to download the latest couple that you were playing when it died to pick up where you left off. Or if four people share a PS4 and play completely different games, maybe as many as 8 games would need to be downloaded which'd be a few days, typically in a household of normal internet usage.
I frequently delete my old PSN titles from my PS3. They are always on PSN to download again should I want, while I also know I'm not actually going to play them again, in all probability.
Oh I agree that you'd download your most current games first, but kids like to play old games sometimes.
And it would annoy me, just having the thought that I can't play a certain game for months even though I legally own it. Simply slotting in a disk seems so much easier.
As a consumer I need to be convinced that a DD game offers an advantage over a physical copy, other that perhaps price, I really haven't heard one with the current or likely near future infrastructure available.