I will give you my takes-A question prompted by this:
Suppose a player is playing Battle Master fighter. The rules establish this character as a tactical expert; but suppose the player - either deliberately, or because s/he can't do any better - plays the PC as tactically incompetent. Does this create an issue for you?
And vice versa: what if the PC is (say) a bard with modest INT and nothing in his/her backstory to suggest tactical acumen, but the player is a strong wargamer and plays his/her PC with very good tactical skill (eg optimising damage per spell slot spent, making excellent risk/reward choices in regards to targetting and battlefield positioning, etc). Do you regard that as cheating?
Battle Master - in my games the rules dont establish the character as a tactical expert, the player does. The rules establish certain capabilities, but their precise "nature" is more fluid. But more directly to your point, just like with cases of many other "skills" I have little problem with calling for a check and telling a player "your character's expertise would tell you..." unless they had established a specific gap in the "expertise" as a matter of story. If they then choose to ignore that, that's fine.
In the second, I do not link the broader INT score (more often Wis for cunning) for experience and savvy at the specific things they do. I am not one to rule that Int is de facto "behind everything" and start to rationalize it as needed for putting on a good performance (remembering songs or your set) or cooking (cuz remembering recipes) etc etc and so I would not also carry that into knowing how to use their other abilities that are not derived from INT stat.
As for the backstory vs decisions in play, I do not have to get into that much, and try to avoid getting into too much backseat driving their roleplaying.
If I wanted a game play where INT was required for these kinds of choices, then mechanically, there would be a prerequisite to gain the benefit. For example, maybe I would add "flanking gives you a bonus to your to hit equal to your Int bonus."
But some fun bits of role play can come out of these. Have seen more than one character where frequently their decisions were "just like in" where the character would reference some book, play, song, history or (setting dependdnt) TV show or movie as their reference for "inexperienced" but savvy play. There have been some more recent nods to this in how MCU has presented Spider-Man suggestion really clever plans based on movies, but it's been around in fiction (and reality) far far longer than that.