PS4 on PS5 will happen.
Sony aren't going to throw away all the current money spending PSN users when PSN is so fundamental to the profit margins of the PS division, which itself is pretty healthy in relation to other avenues within Sony. This is doubly so with MS gearing up and making the Xbox brand far more attractive for consumers.
Yeah that's a good point... although you know what I'd love even more? If we could get PS3 games on PS5. Now, I know the chances of that happening are slim to none, and if so it'd be through emulation so I'd probably need to rebuy my games, but it's still something nice to think about considering there's some amazing PS3 games I'd love to replay again someday, preferably without having to mess around getting my console out with the extra wires and stuff lol. Or y'know, maybe one day they'll add the games I want onto PS Now and it'll then be worth it for me, lol :P