Those who fail to spot something because their passive Perception is not high enough can still roll a check, and they may roll high enough. Passive Perception does not interfere with that.
Yes, but if the DC is set so that those with Expertise or Proficiency + high ability don't notice with PP, then everybody else is going to have about a 20% chance to notice it.
Let's say level 10. You've got +4 proficiency bonus should have 20 in your primary attribute.
The party is:
Cleric with Wis 20 and Perception proficiency. PP is 19.
Rogue with Wis 12 and Expertise in Perception. PP is 19.
Fighter with Wis 12 and Perception proficiency. PP is 15.
Wizard with Wis 13. PP is 11.
So, we can see here that setting the Perception DC to anything less than 20 just doesn't do anything. Cleric and Rogue notice everything DC 19 and below without even trying. However, if we set the DC to 20, then the Fighter's only got a 30% chance of noticing anything with a roll, and the poor Wizard has a mere 10% chance. The Cleric and Rogue have a 50% chance to notice.
Things go from completely obvious to half the party, to suddenly having a 50% chance to miss. That's very weird.
I mean, if your goal is just to eliminate dice rolling, then PP works just fine, but I don't think that's how people play the game. People still call for Perception checks because players and DMs like to roll dice.
Now, if we define PP to be 5 + Perception, and say that Passive Perception is the DC at which something is instantly noticed without rolling the die.
The party is:
Cleric with Wis 20 and Perception proficiency. PP is 14.
Rogue with Wis 12 and Expertise in Perception. PP is 14.
Fighter with Wis 12 and Perception proficiency. PP is 10.
Wizard with Wis 13. PP is 6.
Now you don't feel silly at all saying that the Rogue and Cleric instantly notice something with a Perception DC of 13, as they have an 80% chance of noticing it anyways. The only problem with defining the rule like this is preventing DMs from misusing the rule and saying that the Wizard doesn't see the open pit trap in front of him.
The two definitions would need to be used in different contexts, but, personally, I find the definition used by 5e to be just a waste of time. IMX, list Perception DCs between 13 and 16 or 17 at all levels, and PP as written gives no chance for failure in most parties.
It is also not very problematic if the only thing Passive Perception gives you is additional flavor text that hints at the existence of traps or secret doors or the like without giving the whole thing away.
Except now you're making two Perception DCs. One to get a hint with PP, and one to find it with an actual Perception roll. If PP can't tell you anything except that you have to roll, why bother with PP at all then? It's a waste of time. Just skip it and tell the players to roll! You're going to do that anyways.