Actually, it works just fine - as long as you still have the Daily, your characters ees that opening. Once the player decided to actually use it, he no longer sees it.
Why? Why does he no longer see it, just because he used it once, why can't he see it again. Again that is player run, not character run - the player decided " I am going to use my daily" that isn't the character thinking "I have this thing I can do only once- better use it, so I make use of this opening" - to me (and I know am an outlier here with my playstyle) if the character can do it once, and only once - there has to be a in character, in fiction reasons the character can only do it once - not "only see opening once" not "he is tired out" a specific in story reason, when the choice to use that ability is in character (not player) choice that this thing he does can only be done once.
They could also look very different -the rules are too abstract to really tell, but it can be important for the character - he isn't aware that he's using a Daily or a regular attack, just as he isn't aware whether he rolled a 20 and gets critical hit damage or rolled high on a normal damage role.
That is my other disconnect - the character needs to be aware - if I am making my choice in character in response to in game events (rather than as a player playing a piece in a game) there has to be some way he knows that this 1/day thing is used.
As for your second point - when we play a critical is described by the GM as one thing, and a crit as another. They are not the same thing in story. That is the way we player. Every single mechanic has an in-world explanation for that mechanic, and each mechanic has a different in game explanation.
Not saying that how you describe it is bad or anything, but it doesn't work for me. When I play I make all my decisions in character - if an ability or resource is being used I chose to do it as a player, because my character decided in game to use that resource. Dailies without an in-game reason that the character knows and understands just doesn't fly with me. Anything else takes me out of character and thinking like the player at a table, and getting into the mind of the character is the whole reason I game.
If you can give me how the character would describe in world using in world speak how that daily is being used, I'll be happy to listen. One could say "I cast a fireball" in game. One could say "I pull out my holy symbol and turn the undead" in character. How does a daily fighter say what he is doing - in game - for a daily that is using "only sees it once" or "is too tired afterwords" for their justification. Notably without stepping on the GMs side and saying "he has an opening I exploit" the character cannot create said opening by use of the power. And if he can, why can he only do it once.
That is also a problem with the "too tired" thing - if he is "too tired" to use the daily, but has another ability with same in game effects, then why is he too tired for one, but not the other?
For me it is all about in game realism - the kind of abstraction necessary for the player to control the character in game without in game justification pulls me out of character and makes playing less fun.
I love a fighter to do cool things - I really like the concept of the combat superiority dice to give fighters in game toys, but I've never been able to gel non-in-fiction limited resource with out-of-fiction limited resource. I see the rules as the rules of the world - if something only happens once a day, it is physical law of the world that it only happens once day. I just can't mentally bring that together with dailies that don't rely on in game fiction to explain the limited resource.
I realize I come off a bit argumentative for which I apologize*, but if you can actually solve my dilemma I'd love for it to be done. My playstyle is very much in fiction/in character - I've had games where this kind of thing has kept me from enjoying it.
* It's an approach to gaming I feel passionately about so I tend to get intense.