Also, when I come into possession of a new PS4 disc, I immediately insert it into my PS4, so it starts installing and downloading any updates as soon as possible while I'm off doing something else. If I want to get something from PSN, I just do it on the app and remotely download it to the PS4.
Basically, I've gotten to a point where pretty much anything I do with the PS4 that doesn't involve actually playing a game... is done outside the PS4, so usually when I'm ready to start playing a game I can just wake up the PS4 and start it. The only downside is I have to pretty much always leave it in rest mode. I think of it like my phone, which I rarely shut down completely.
This is actually a bit of an advantage over PC if you don't keep your tower turned on. You can't remotely cold boot it like a modern console and hibernation mode is finicky. Even though physical discs are disappearing from PC, the few times I do install one these days make me feel like I'm traveling back in time.
Here's the deal: consoles are pretty much becoming closed-software computers designed for TVs. Mobile devices sort of won the computing war because they figured out how to make the hardware and operating systems accessible to everyday people. You wake up your phone, you tap and app, and it boots. Consoles need to figure out a similar level of accessibility. The main problem, really, is dealing with pieces of software that are over 50GB.