Bill Zebub
“It’s probably Matt Mercer’s fault.”
"What thing?"
Commander's strike is a mechanical manipulation of trading a die and an attack for allowing someone else to use an attack out of turn and hit harder. There is nothing narratively to point to and say see the superiority die in action, that cannot be attributed to non-superiority die stuff narratively.
Narratively it is Lancelot saying "Get him!" and the ally attacking. That narrative could be a commander's strike or just Lancelot encouraging an ally in a melee as the ally attacks.
I will acknowledge that there is a difference:
1) The fighter might not "know" he/she did anything special, if you want to regard the mechanic as a pure metagame construct, invoked by the player controlling the marionette strings.
2) The wizard, on the other hand, "knows" they performed some magic that resulted in the web spell.
And I don't think that makes a difference for what we are discussing: that is, whether or not the character is aware of a restriction that has a 1:1 correlation with the rules. The fighter's player could just as easily fluff expertise dice so that they do represent a player decision. That is, Lancelot knows exactly what that "thing" is, and from there he might also know that...because of "reasons"...he can't do it more than 3 times before he has to take a nap. Now, I recognize that some people hate this idea because of that "dissociative mechanics" canard, but it's logically consistent and valid.
So regarding a fighter you can imagine it works either way...the character is or is not aware of the restrictions...and while you may have an aesthetic preference, that's all it is.
The same is equally true of the wizard: your wizard can be aware of the "rules", or not, and it all still works. It's just a matter of aesthetic preference. Anybody who insists that the wizard has to be aware of the limitation, and the fighter can't be aware of the limitation, is confusing their preferences with facts.