Passive perception is also used to notice traps and secret doors if no one is actively looking for them.That's fine, but that's also my point. By RAW you use passive perception very rarely. Its primary use is to determine if you're surprised by someone stealthing.
I'm not aware of any general uses for passive Investigation, but I believe some specific cases might pop up in published adventures.
In the interest of saving time, a DM might set a PI threshold to figure out how to open a secret door whose existence is already known. Not much else comes to mind.