The question is only: Do you avoid using 4E powers if the effect doesn't make sense to you in that moment in the fiction?
I voted no... and I played/ran 4e for 2.5 years... until my group moved on to Savage Worlds and AD&D.
My group cares about the game fiction. A lot. But most of us think it's fun trying to fit the powers (mechanics) into the game's fiction --call it description, rationalization, justification, apology, the opportunity to show how clever you are, whatever.
The thing is: any system is going to generate unrealistic results (older edition of D&D certainly did). Reconciling these results with the in-game reality (ie, fiction) is a central component to RPG play.
If it seems counter-intuitive, I find a way to make it make sense.
Exactly!
So if someone in your game needs to break down a door, why don't you check his Wisdom score? Checking for Strength would be too realistic, right?
A Strength check makes sense to resolve
battering down a door.
A Wisdom or Int check would make sense to resolve opening a door by removing its hinges, or some other non-brute-force method.
It all depends on how you frame --pun unintended-- the question, and to what extent you use ability checks to overcome various obstacles.
Note the same logic applies to using different ability scores in combat: a STR fighter uses raw strength, an INT fighter fights well,
smarter, while a WIS fighter relies on determination and/or faith. It's all in how you abstract things.
And if a dwarf with 3 Charisma and no social skills whatsoever wants to seduce the elven princess - more power to him! Who cares about "realism"? It's just a fantasy game, right?
I'll admit love at first sight is probably out of the question for a CHA 3 dwarf with no social skill training -- unless the elven princess has a scarred, surly, midget fetish

.
However... what if it isn't love at first sight? What if the dwarf just rescued the princess from orcs, or saved her father from assassins? What if the dwarfs CHA of 3 represented his complete
honesty? That would also explain his lack of Bluff/Diplomacy ranks...
Plausible, no?
I've got a simple rule when it comes to RPGs. You can either spend your time and energy figuring out why thing work, or why they don't. Which is more fun, and more appropriate, in a game about pretending to be an elf?
I also have problems with PCs swinging melee weapons with Con or Cha.
It works for paladins. CHA represents a measure of their god's grace, which strengthens their arms as they swing their weapons. It's seems appropriate to me.
I mean, CHA has traditionally been the "paladins stat". An AD&D paladin needed a 17+. It affected how much a 3 pally could heal *and* it determined their to-hit bonus on a Smite, which is exactly analogous to 4e having CHA-based melee attacks.
Hmmm... come to think of it, I did *nod* at realism when creating my 4e paladin. I gave him a decently high STR to justify his use of plate armor. It seemed wrong to gad about in so much ironmongery with a STR of 10. However, his CHA-based melee talents didn't bother me in the slightest. Nor did his melee power that attacked WILL instead of AC. In fact, that one led to a long-running joke at our table: "I stab him in the
faith!