I finally went digital with PS4/XBO because I realized it was like buying big box PC games in modern times. When you buy a big box PC game, you are installing it via disc, it goes on your hard drive, in most cases, it gets tied to some kind of digital service and then they force you to put the disc in to verify you actually own the content. Essentially, you are just buying the disc as a distribution method instead of downloading it. It's still a digital game when it comes down to it.
With PS4 and Xbox One, it's basically the same thing. You get the disc but you have to install the game and get patches for it. The version that's on the disc is instantly outdated and the game doesn't play off the disc. It's completely dependent its digital counterpart. The only reason to own a disc for a game is if you like to sell or trade your games (I don't) or have a box to put on a shelf. For cartridge based games and/or pre-internet consoles, I would absolutely own the physical versions. For modern games, they are pretty much digital whether you like it or not.
All of that said, I treat movies completely differently. Movies on disc are better versions than what's available digitally and are not bound to particular machines like consoles. If I want to watch some obscure Criterion movie, I either have to track it down on a streaming service and watch it in mediocre quality, find an illegal download, OR, I can simply own the movie on Blu-ray in its best possible version and have it forever.
A game on disc is the same game that's available digitally (minus the patches). With movies and music, there's still very much a reason to own them physically since the quality varies. With games, those reasons are dwindling beyond just wanting to physically have something in your possession.