Showing Dice Rolls: Why and When

I know, you saw the title and you may be thinking, "...didn't I just read your diatribe on why GMs shouldn't hide rolls...?" Yes. But I RP as a hypocrite IRL, so I'm just doin' what my character would do, bro.
Not really. So, I do roll privately for passive checks. My reasoning is, as was said in another thread, every type of game inherently has inescapable "metagame moments" - or metagame-type thinking imposed onto those playing. One of those moments concerning TTRPGs or DnD specifically is when the players are at a scene/encounter/etc in which the players could gain a resource(an item, intel, information, etc) if they only knew to ask the right question or do the right action. Times where their character would know to ask or do the thing, but not the player.
When that happens the DM usually or should ask the player to make a roll if not outright tell the player what their character would know/do/gain in this situation, IF it were something the character would know naturally. But what about times where the character wouldn't naturally but through effort? You'd ask for a roll, naturally. They failed the roll. Well, fuck. Now the player knows something is up or something isn't as it seems or they may feel like they're missing out on something - essentially it would have been better to not even have asked them to roll. They'd be having more fun, rather, had this just not happened.
An example will explain better than I am right now, I think.
The party of two just entered into a tavern. Unbeknownst to them, the Tavern is being run by someone with a disguised self on. One of the party members is adept in the arcana, reasoning they may be more sensitive at sniffing it out.
Now I could ask the player after they meet the tavern owner "Roll a perception check" or whatever. But now the players know, something is up. So now they are on edge, and suddenly despite nothing narratively have to change, the party of two who a moment ago was comfortably and non-chantilly going about this tavern are suddenly wanting insight on EVERY patron, don't trust the food or the people next to them, all simply because I asked for a perception check.
Rather, I would check the one adept in arcana. His passive perception is 15 "Okay. Let's see if he's proficient in anything that would be of help - oh I see he is in arcana. I'll add 5 to his passive Perception. So 20." I now make that the DC for deception check for the tavern owner, OR I would do a roll-off between the player's perception and tavern owner's deception, giving modifiers for proficiencies or other outliers that would affect the situation to the best of my judgment. Up to a +5 or advantage.
Now, passing or failing this roll never gives the player anything. It instead adds a decision to the scene. DnD and the fun therein come from the decisions the players make. Not from giving them things, remember that.
Depending on the magnitude of the fail or pass, matters simply because I like how dice can tell a story.
So say they failed, by less than 5. I would tell the player something the tavern owner did/say/or SOMETHING that if the player is sharp, would feel is out of place. Maybe a phrase or a tick, or some mannerism that hints at a different origin than presented.
Fails by 5 or more, I wouldn't tell the player anything.
Pass? I would tell the player they can sense the weave but it would require more focus amongst the tavern business to zero in on it or whatever ya know? Something that would inform the player "Hey, your character would naturally be sensitive to this magic going on, but you as the player wouldn't." So instead of the player missing out on something and, most importantly for me, instead of the player doing perception checks on every fuckin encounter - they'll know when to ask for rolls that fit the narrative without bogging down play with roll checks and stuff.
The benefits are three-fold here. You avoid the aspect of revealing info to the players that would change how their characters act - meta gaming.
You avoid the players asking for rolls non-stop. Because whether you allow them or tell them no you can't, pointless rolling leads to rolling becoming pointless, get me? If you tell me I can't roll whenever I ask, but you've also shown me times a roll - had I known to ask - would have led to decisions - I'll feel cheated. And on the other hand, if you do allow me to roll, but each time leads to nothing since there in fact was nothing - I'll feel you are just making it nothing because I asked. Because you're the DM! You could have made it be something even if it wasn't but you never do? (or so I feel) I'll again feel cheated. And in that situation, the DM will become exhausted constantly trying to think up things that were "hidden" when there wasn't. I am rambling, so TL;DR.
I roll privately when there are situations a PC would know to attempt something that the Player may not, but when I don't want the act of asking for a roll to influence the player's actions. If they "pass" the roll, I then will hint at what the PC would know or do, letting the player then decide. The PC's knowledge in-game influences the player's action out-of-the-game in a way.