With the amount of time it takes for some titles to become playable, without having them installed first? I see disk space becoming a problem very quickly. If I go back in my game collection and want to play game X again I don't want to wait half a hour before I can play said game.
Needing to remove games from my HDD would prevent me from playing older games. As it would be a chore to first uninstall another game to make room for the game I want to play only to wait 30 minutes before the install has progressed far enough for me to play the game.
I get that it will not be enough for everybody...
But the console does have enough space to have quite a few games installed at once. I have 11 installed games right now, and I'm just barely over 50% full... This include games that I already finished like Ryse, DR3, Max... and has no current plans on play them again anytime soon.
In my case, the overhead of installing the game wouldn't be an issue either, because I don't usually start the console not knowing what I'm going to play, if I ever want to revisit any of those games I would queue them to install in the morning, go to work, and when I'm back home they would be already installed and updated...
Like I said, I get the need for more storage, but I think many people will be fine with the provided space (assuming game sizes doesn't skyrocket as the years pass by)... In some cases having better tools to manage content (like using smartglass for managing your library even when you are not home) should be more useful to users than straight up having more space.