Why shouldn't he? There are many in game reasons you can use like weaker armor and having trouble to penetrate heavier armor with his fighting style.
None of which apply to most class-and-level systems, certainly not D&D, and none of which were listed as things the player wanted.
'sides, even if your rules apply for some bizarre reason, you should still be able to use your skills effectively - use your cloak in your off-hand to swipe at their eyes so they can't see, trip them, try to slip your blade between plates of the armor, etc.
And what when there is no chance to talk the enemy down or it doesn't make sense?
Welcome to GMing 101! In today's class, we'll be talking about encounter design.
If the GM only comes up with encounters where it is impossible for your character to contribute, talk to them about it or find a new GM.
Or do you keep track and will railroad the players into an situation that can only be overcome by talking?
Similarly, if the GM comes up with encounters where it is only possible for one character to contribute, talk to them about it or find a new GM.
Will you as DM make sure that this never happens and deny the player to explore this part of his character? [emphasis added]
You may have fun being the party's wheelbarrow, but that's probably not something most people enjoy.
Where did I say something like that? That rather fits your way of thinking where combat ability has to be bought with non combat usefulness in order to be "balanced" on paper.
Actually, I don't like trading combat for non-combat effectiveness at all. You're the one saying you should be able to sell your combat ability! You just... haven't offered what you should be selling it for. So... good on you for disliking your idea, I guess?
If you'd read my posts, you'd know that I think all characters should be able to contribute in all the distinct parts or sections of a game. This means that the mage researching otherworldly creatures gets help from the swordsman reciting folklore and fairy tales he heard in his youth, and the footpad gets to talk about the rumors he heard down at the tavern, and the woodsman gets to mention the strange tracks and mutilated animals he found in the woods a while ago. Similarly, in a physical fight, the mage gets to cast spells, the swordsman gets to show off his skills, the footpad gets to knock people up the back of the head with a sap, and the woodsman gets to talk to the brainwashed enemy and try to convince him something's wrong with himself.
Or something.