So you're saying if they search and there's something there to find they'll auto-find it? As a player I'd break that in one action declaration: "I'm searching everywhere we go, as SOP".
"While you're searching the room, the monsters chasing you catch up with you. Roll initiative."
"Wait....what? We were fleeing, I didn't say we stopped to search the room!"
"A while ago you said you search everywhere you go, as SOP."
"..."
So, yeah, another thing I used to do in 1980 but don't anymore is play with standard operation procedures declared at the beginning of the dungeon.
If there's no chance for me to miss things when I search, I've just blown open every secret the place has, which is very quickly going to discourage you-as-DM from placing secrets in your dungeons. And where's the fun in that?
First, there's a time cost to searching, which actually works pretty well in games that have good mechanisms for it (I mostly play Shadowdark, which does.). So sometimes you will miss things because you choose not to search.
Second, in some cases you will have to be very specific about what you search in order to find the secret, but those cases should always contain a tell.
But you do get at a deeper question, which is how to hide "secrets" in a roleplaying game. For a long time I played by gating secrets behind RNG. "1 in 6 chance to notice secret doors" etc. But that's not actually very fun. Playing D&D itself was fun, and random dice rolls to notice things was part of D&D, so I didn't question it. But, really, randomly discovered secrets don't add any fun. Getting a lucky die roll is not
accomplishing anything. As a junior high DM it would torture me when my friends missed the secret door to the treasure room, so invariably I would keep dropping hints until they went back and found it. (I'm specifically thinking of module G1 here.)
As others have noted in this thread, "Traps suck." They really do! And secret doors, too. They are incredibly hard to do well in an RPG, but in my opinion that doesn't mean we should just give up and ask for a Perception check. It means we should use a lot fewer of them, but take the care to design them well so that they are telegraphed, they require problem solving, the solutions require risk, and the players feel like they've actually accomplished something when they succeed. And they also feel like it's their own fault when the fail, rather than just arbitrary resource loss imposed by the dice.
A while ago I was running a long adventure and my players eventually realized "there must be another level below us". I think they spent the entire session trying to find the entrance to it. They eventually narrowed down where it must be, and my description of the location triggered a memory of something they had found in another location, so they dug that up again, deciphered the clues, went back and performed the correct sequence. When I said, "Click," they burst out cheering.
I'd rather have one of those every 10 sessions than a bunch of randomly discovered secret doors.