Perception and Insight are the only skills that have passive scores. Those passive scores are generally used to set DCs for other characters’ hide/deception attempts (there’s a very long thread here somewhere discussing whether or not they also set a floor for active perception and insight checks, but that’s neither here nor there).

If the circumstances of the task and the actor are such that there’s not really any reasonable possibility of failure, then there’s really no reason to call for a check at all. But that decision is based on a lot of factors other than numbers, and it’s always up to the GM on a case-by-case basis.

It's a matter of interpretation, and I think it may be deliberately vague in the official rules.

Personally, I use passive Knowledge skills for remembering or recognizing facts ( Arcana, Religion, Medicine, etc. ).

In my mind, Players only roll when they are actively doing something, so - for me - Perception is almost always Passive, and Investigation - an activity - would never be passive. Skills that could go either way, sometimes I roll and sometimes I use passive - and sometimes both. E.g. - the Party runs across a tribe of Orcs which have expired from some disease. The Wizard is proficient in Medicine, so I check their passive Medicine score ( yeah - technically that isn't an official thing for many people ) to see if they automatically recognize the symptoms of the disease. If they fail, I'd allow an active Intelligence check ( with proficiency bonus, since they're proficient in Medicine ), if they conducted an autopsy, or otherwise did some sort of active medical investigation.

Likewise, for Arcana - if they didn't recognize a spell effect they saw on an adventure ( because the DC exceeded their passive Arcana score ) - I'd allow an active roll, if they got back to a research library and attempted to research the effects they saw ( although I might do something insane like average their bonuses for Investigation and Arcana - since this is really an "arcane investigation" ).

This approach really streamlines a lot of die rolling that I see as needless ( others may disagree ). Players walk into a room, their Passive Perception, and Passive Knowledge skills are high enough to have spotted X, and understood Y - so I just tell them.

What this approach loses, however, is the chance for critical failure, or critical success. That may, or may not, be a fair trade off in the eyes of the Players and the DM.

To me Passive/Active is tied to the actions of the Character: are they expending effort to do a thing vs. are the remembering / recognizing / intuiting a thing. Only when the Character is actively expending effort, does the Player get an active roll - at least in my sessions.

Clearly you approach it differently; that's OK. You're treating Passive scores as as floor to an Active roll ( something I believe Jeremy Crawford has advocated on Twitter ), whereas I'm treating it as an automatic roll. I don't stack Active checks on top of Passive, unless there is a change in approach, level of effort, or circumstances - where it appears that you allow an automatic active roll on top of the passive check. Your approach is the functional equivalent of having the Player roll actively all the time, but taking their passive score or their roll, whichever is greater, as the skill check result - although you skip the actual die roll if they can't fail.

I agree with most of your point about not needing a roll when there is no time constraint, risk, or resource consumed. The example I use is the idea of a Rogue picking a lock, to a deserted mine, in the middle of forest, with no one around. They will get through the lock. They can just keep trying until they get it right. However, I do still call for a single roll, which does not determine success or failure, but time needed, and clues left behind. The Rogue is going to bypass the lock, but if they roll a Nat20, then they do it in a few seconds, and leave the lock pristine ( so the bandits won't even notice that the lock has been tampered with ), but if they roll a Nat1 then it might take them 20-30 minutes and scratch & mar the lock to hell, making it clear that someone has been futzing with the lock. Pacing wise, it's identical - I just narrate what happens - but consequence-wise later in the Narrative, it might matter when the Bandits arrive @ the mine.

Here's a reference that got me thinking about this ( or at least, one among many ): https://theangrygm.com/ask-angry-passive-skills-active-skills-perception-and-knowledge/

As one of the players in this group, I will say that it's certainly different than how we have been playing (though I've only been playing for 1.5 years now), but it's a nice change, I think.

While we roll dice less (boo!), we have more chances to succeed (yay!). At least, that's what it feels like.

I've noticed it makes my taking the Observant feat super useful, and I'm very happy I took it.

I use passive perception through each session. The player going into a room or area I use passive perception to determine what they initially see. Then they can investigate from there. Saves on a lot of rolling.

For me saying "you walk to a an open door to a room.. roll perception.." sucks. No need for that so passive is used to replace that stuff.