Damaged disc = corrupted install. Corrupted install = rebooting your PS4 in safe mode and rebuilding the HDD database.
In my experience it's mostly companies like EA, Activision, or Ubisoft that uses the disc as just a download code. Luckily I don't play games by them.
I thought as much. Again, on Xbox, even if you take the disc out, it still installs. I remember putting in a disc, letting it install 1%, removing the disc and putting in another. I'd have like five games installing at once with no disc in the system at all. When I tried to play an installed game, it would ask for the disc or ask me to buy the game digitally. Buying a game digitally just meant I didn't need the disc anymore. And, as many already knew, XBO games install muuuuuuch faster if you take the entire system offline and then install the disc. I have my own theories as to why this is.
PlayStation is a different beast. The disc and the digital games are two totally different things. But I feel like, if you can just rent a game and install it (or borrow it from a friend) even a damaged disc will let you access the install.
This whole thing is way off topic from the op. Shouldn't have to buy a game and worry about it being damaged. The only games I've ever ordered online were Gravity Rush PS4, Bulletwitch (360), some random DS games for my daughter, and some GameCube games I missed back when the GC was still alive. Never had a problem, though. Everything always arrived in great condition.