The advantages are obvious, I won't dispute that. And these days, with so many digital game purchases, game ownership is already a bit of an illusion. Certainly in my case, if I had to guess I'd say well over 90% of my purchases have been digital in the last +-5 years. But at the same time, I still have a working PS1 lying around with a decent collection of working games. I will admit I almost never touch them, but still, I feel comfortable in the knowledge that if I feel like it, I could simply fire it up again. Just as I don't feel comfortable in the knowledge that, if they would choose to, Google could shut down a 5 year old game if it was really unpopular or something. It might never happen, but it's still an uneasy situation.
And one other case to consider: PT demo. This was pulled from the PS Store, so you can't get it anymore. Yet I'm still able to play it, as I have it installed on my PS4 HDD. I even transfered it to my new HDD when I upgraded to PS4 Pro. In the world of game streaming, the decision to pull the game would mean I'd never be able to play the game anymore. That's something I just can't accept.