I mean… that is what happened on PC. I know people forget we exist, but basically anyone who was “a gamer” back in the early 00s embraced digital distribution and Steam for a reason. Because after the third time that you have done four disc swaps and entered three 30 character keys to play Neverwinter Nights 1? That shit gets REAL old. Same with needing to be aware of what order to install what patches so as to not brick Dawn of War: Soulstornm and have to reinstall everything.
Contrast that with double clicking something in fricking Impulse and then waiting 30 minutes for it to install.
Which is kind of what you described with the Vita. Nobody wanted to have to carry two or three UMDs with them anywhere they want (let alone the rise of indie games that never had a digital release). Tinfoil, but I strongly suspect Nintendo made a big deal about not licking cartridges so that the Jeff Gerstmanns of the world would… lick that shit. Which led to the meme and people wanting to buy cartridges.