A few questions I can see coming…It might be worth examining why your players think they need to optimize their Perception. It could very well be with how you are presenting exploration challenges or how often monsters are trying to surprise the PCs. In my games, it's a good choice, but it's not the best one - it depends. And that feels about right to me.
It doesn't actually remove gating information. Gating information in this way doesn't really exist in the rules, so that's all on the DM, perhaps a habit learned from previous editions of the game. So the DM doesn't really need a house rule to fix this. They can just stop doing it at any time.
If there is (1) no gating of information that should be fairly obvious in the environment and which telegraphs threats or opportunities, (2) not every monster is trying to gain surprise, and (3) the DM asks players to establish a goal and approach when they ask to roll, then I find this all goes away. I tell players straight up that I cannot and will not assume what their characters are doing during a challenge and that without a goal and approach, I can't determine whether a check is needed at all. I add that if the approach to the goal given the context is efficacious enough, then they won't need to roll which is a WAY better outcome than trusting a d20. So it's to their own benefit to be reasonably specific, in addition to being easier and more entertaining, generally speaking, to everyone trying to build a story together.
I wouldn't expect you'd get much pushback at all. My objections are purely around it looking to me like a downstream solution to a problem that is happening upstream. And I'm the sort of guy to want to fix the problem at its source than apply a patch that may have unintended consequences.
If perception becomes a saving throw, is proficiency coming from class or choice of skills? If class-based, which ones? What about elves? What of Resilient feat? Or Expertise? Any way of acquiring proficiency at a later point? How should it interact with observant feat? Do Skulker and Dungeon Delver(?) feats interact with perception, can’t remember.