I have the feeling in most RPGs, Perception is one of the most important stats to have. It might be a bit more important in D&D 5 because usually every player can roll perception, in some games, there might be a group perception type of rule or something. But if you don't see where you're going, if you don't find what you're looking for, you're a bit screwed and will only randomly stumble into things ,including traps and ambushes.
It's probably no accident that Pathfinder 2E removed it from the skill list and made it something seperate, though I don't really feel like it mattered much in the end. (That it is also the base stat for initiative probably did).
I am also thinking of Night's Black Agents or the gumshoe system where you don't need to roll on perception to find clues and the like. You just need to be in the right area to find it and state you're using your ability, and you get the clue. Because it's easy to run a game into a corner if the important clues the party needs to find to solve the mystery are only accessible via Perception, and they miss their rolls -they went to all the right places, talked to all the right people, but the dice say they failed anyway! Instead, they still need to do the legwork, but it's not luck that decides their success.
In Shadowrun, I'd rank Stealth at about the same level, because you really don't want to waltz into every compound and raise the alarms. D&D is a lot more foregiving here, one or two scouts are sufficient most of the time.