I've never not had a game in my 3DS except the small space of time when I'm changing games, which is rare. Pokemon Black has been in my 3DS for about 2 years now, I'll finish the 2nd half of the game so I can transfer all my Pokemon sitting on Pearl up to the bank some day....never had an issue.
Phantasy Star Nova is pretty much permanent in my PS TV except I move it to my Vita when I go on a trip and bring the Vita or the extremely rare occasion I have another physical game. PS Nova pretty much is the default game because I'll finish it some day, dammit, and only got it physical because it is an import and I don't want to fuck around with the Vita store region shit. Also never had an issue.
Consoles, discs (or Switch cards) will stay in there until I finish my playthrough or I need to pop in another disc for some reason (ex: random Smash Bros matches). Never had an issue, though a bit of me is paranoid it will not turn back on and now it has my game inside forever.
I will not leave the discs out, though, only monsters do that. Either in console, in case, or other protection (3DS/Vita multi-game card holder)