There seems to be a lot of people misunderstanding passive checks, they seem to think there is an "active" vs "passive" dynamic, where you only use your passive score when not trying to do something this is wrong.
"Such a check can represent the average result for a task done repeatedly."
This doesn't mean that the person looking for secret doors isn't actively searching or the guard on watch isn't actively keeping an eye out, it means you are using the passive score to represent repeated active use of the skill.
"or the DM wants to secretly determine whether the characters succeed at something without rolling the dice."
This is why every ability check has a passive score, the DM can speed up play and just say your passive Athletics is high enough to climb the wall without a check, or your passive Arcana is high enough to know about this type of magic portal, or passive Perception is high enough to notice the gnoll trying to ambush you.
If you want to represent a person who is not trying to look for things that isn't just passive perception, that would be passive perception with disadvantage. Passive checks are for repeated use over a long time, and for the DM to just use as a guide to let characters auto succeed.
PASSIVE CHECKS
A passive check is a special kind of ability check that doesn't involve any die rolls. 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.
Here’s how to determine a character’s total for a passive check:
10 + all modifiers that normally apply to the check
If the character has advantage on the check, add 5. For disadvantage, subtract 5. The game refers to a passive check total as a score.
"Such a check can represent the average result for a task done repeatedly."
This doesn't mean that the person looking for secret doors isn't actively searching or the guard on watch isn't actively keeping an eye out, it means you are using the passive score to represent repeated active use of the skill.
"or the DM wants to secretly determine whether the characters succeed at something without rolling the dice."
This is why every ability check has a passive score, the DM can speed up play and just say your passive Athletics is high enough to climb the wall without a check, or your passive Arcana is high enough to know about this type of magic portal, or passive Perception is high enough to notice the gnoll trying to ambush you.
If you want to represent a person who is not trying to look for things that isn't just passive perception, that would be passive perception with disadvantage. Passive checks are for repeated use over a long time, and for the DM to just use as a guide to let characters auto succeed.