So I can see how someone might get there, but that's a very steep cost for a pretty shaky reason in my view. Making it a straight bonus action is probably a good enough deterrent to the skill check pig-pile. As is making sure there's no expectation on the part of the players that they get to make checks for things at will. If the character background doesn't suggest having specific knowledge of a monster, the DM is well within his or her rights to say "No roll, you just fail to recall anything."
I just have the whole party roll at once, at the start of combat, or I just use their initiative rolls. I use the 4e monster knowledge checks as a vague guideline for what skills tell me if they recall something about a type of monster, and I just have them keep their dice as they rolled them while I jot down init order.
Any init rolls that are high enough that I think there might be a chance of success, I ask what their skill bonus is for the relevant skill, and add that, and check it against the arbitrary DC in my head. It takes about a tenth as long to do as to describe.
I allow bonus action Investigate checks to examine an enemy to figure out it's weaknesses, especially if circumstance feels right for an observant person to see a clue and be able to deduct something useful.
As for the background part, I really dislike that. IMO, players should feel free to establish bits of background during play. I don't expect them to run through an exhaustive metagame excercise pre-game, where they try to think of everything in the game that their background
could be relevant to, and make note of anything at all that fits, and then that is it. I imagine I'd have no players if I did that.
But, without that, such a system, if it can be called that, puts the player character's competence and history into the hands of the DM's "common sense", which means nothing more in reality than that individual's intuitive, subjective, sense of the world. I don't like the idea of a player character's knowledge of something being determined by the vague intuition of someone other than the player of that character.
But maybe I'm using incorrect assumptions about what you meant? Idk, I'm just a guy. lol
Either way, I see what you're saying. If a player thinks their character should know about Lich phylacteries, in a campaign world where Liches are a new or long forgotten thing, and only the equivalent of old candlekeep scholars would even know the basics of what the hell a lich even is, that player needs to explain why their character would know that, and if there is no explanation, it isn't a check. At most, they could Investigate the problem, if something in the world indicated that there is something to investigate.
Which segues into a thing Ive been thinking about a lot lately.,
That is, "metagaming" as a way to make up the difference between character competence and player knowledge/intellect. But that is fodder for another thread, I imagine.
edit: forum bugginess on my browser lead to cross tab multi-quoting, and then cross thread multi-quoting. fixing it now.