Technically, 3e already did this.
I agree with TwoSix, including that this is (as best I can tell) the same as 13th Age.Yes, but the difference with this suggested system is that the 3e rule was simply a rename, whereas the "player-phrased skill" (which I'd say is almost identical to 13th Age's backgrounds) moves the use of a skill to negotiation between the DM and the player.
The move from skill lists to free descriptors is one of the better features of 13th Age, and something that 4e would benefit quite a bit from in my view. It's not as good for those who want to play resource-management and system-mastery based games, though. They probably want to stick to the lists.