So going off of these parts of passive checks
"Such a check can represent the average result for a task done repeatedly, such as searching for secret doors over and over again, or can
be used when the DM wants to secretly determine whether the characters succeed at something without rolling dice, such as noticing a hidden monster." (PHB, 175)
"Passive Perception. When you hide, there's a chance someone will notice you even if they aren't searching." (PHB 177)
The section on passive perception versus stealth shows that the person just notices without even trying, which is different from "oh I'm gonna keep an eye out." You just innately and immediately see them. This infers that this innate form of passive check can sometimes activate without the player saying anything.
So the issue is, when does a player have to state they're attempting a skill before the passive check kicks in?
Like, I could see if a passive insight check beats a deception roll, the person realizes they're being told a lie, without first having to say they're trying to use insight on the person. While you lose the part of the game of player's having to carefully consider each part of the conversation to see which parts they want to call insight on, some player's could just state "I insight them every time they tell me something.
And then if it's like an intelligence check, should a player first have to state that they want to make the check? Is it they walk into a room with an obscure holy symbol on the wall, their passive religion checks beats the DC to recognize it and "as you walk in, you see a symbol on the wall and immediately recognize it as the holy symbol of 'so-and-so'," or do you wait until they state that they want to examine the symbol?