Title? I don't need no stinkin' title.
I think that's the difference. I don't want the players calling for a check. They might not need to even roll anything, never mind that 5E doesn't have skill checks at all. I'd much rather have the player explain to me what they envision the character doing. It can be third person like a movie director instructing an actor, and then working with me to determine if a check is even needed.
If a player says "I'm going to roll Insight!" my response is going to be "What do you envision your character doing?" or "What is your goal?" The response will determine what the next step is going to be. Players might respond: "I want to see if Ned is hiding something from us" or it could be "I want to threaten Ned into talking to us and tell the truth." The first one is Wisdom (Insight) the second is probably Charisma (Intimidation).
I'm never going to make a player try hard to use the buttons and levers they have access to, but I want to be clear about what buttons and levers they are trying to use. Sometimes abilities and skill proficiencies are important, sometimes literally describing either by accident or design the answer to a problem results in the solution working (as with searching a room for example).
Except that there is no visible action. The activity is pretty much mental, paying close attention and thinking about what is being said. You can come up with all sorts of words to describe that activity, IMHO "Can I make an insight" is just one way of describing what is always going to be an internal mental process. Threatening Ned is not an insight check, it's an intimidation check. It's unrelated.
I've never had a DM have this kind of attitude which is one of the reasons I started this. It seems to be a big deal ... but only on this message board and never in the real world.
Let's say I consider my PC an incarnation of Sherlock Holmes. He watches people closely, deduces things about them based on what they're saying and how. If he's trying to intimidate, persuade, badger or console the NPC that's handled completely separately (possibly with it's own check). How many ways are there to say "I observe them closely to intuit their emotional state"?
If a PC were doing ... I don't know ... an investigation check of a door to look for traps, I'm going to tell them any info I think they would get from examining the door closely. Maybe they notice that there's no trap, but the lock is new and high quality. Or there are minute scratches on the lock indicating that someone else has tried to clumsily pick the lock. Or any number of other things. I'm not going to withhold information that's unrelated to traps. All I need to know is that they're examining it closely.