When I was a kid I got a used copy of a Hamtaro game (aka the legendary story of me getting this Hamtaro game over the Minish Cap and why I never got to play TMC until I was in high school on 3DS Ambassador), and I was so thrilled about it, I didn't care that it didn't have a case. I think it being a cartridge made it easier to manage without a case, and at that age, I didn't really keep my games in their original boxes, period. My parents usually had me throw away the packaging before DS games introduced them as a more permanent package. I have a lot of homeless games from my childhood as a result of that, even if I was the original owner.
As for now, I don't think I would like a game without a case, or if it came without one, I would give it one. I like shelving my games, and cases make that easier. But it's probably more critical for discs than cartridges as storing them without a case probably poses some risks to damage them. My only used game that was a disc was my Gamecube copy of the Wind Waker and it did indeed include a case. The case is a bit scuffed but it's otherwise in fine condition with the manuals, and I'm glad to have that for such a special game like the Wind Waker.
Overall though, I think it probably depends on how much you want the game and the sacrifices you'd be willing to make to own a physical copy of it. But if it's a really special game, then it feels a bit like an injustice if it doesn't have a case to call home. unless of course its permanent home is inside your console
