One of the arguments I've heard against relying on player narrative where character skills are concerned is that it rewards players who are good narrators at the expense of those who are not. The counter argument, which I seldom hear, is that relying on a numerical system to resolve skill use rewards players who are good number maximizers at the expense of those who are not. By favoring one approach over the other, aren't we just swapping one type of player talent for another?
I've played both approaches--games where every action had an associated number on the character sheet and almost nothing was narrated, and games where characters had no ratings at all beyond a name and a concept, and every action they took involved negotiation between player and GM. In my experience, the presence or absence of rigidly defined character abilities had little impact on whether I enjoyed the game. More than any other factors, my enjoyment depended on who I was playing with and how well the GM handled the session.
That might sound like a cop-out, but RPGs are funny animals. They violate many of the conventions by which we define "a game." I've argued that D&D isn't really a game at all; it's a structured play activity, more akin to building a tower from wooden blocks with a group of friends than to playing parcheesi or Pandemic with friends.
In that regard, isn't trying to shoehorn the standard conventions of games into an RPG a disservice to the RPG? Is it analogous to trying to force elements of poker into chess? Choker might turn out to be a fine game, but it would not be chess, and I suspect that the hybrid would lack the spark that makes both chess and poker shine so brightly.
Experience confirms to me that players who enjoy narrating their characters' skill use are good at narrative, while players who prefer numbers are those who manipulate numbers well. Nothing's wrong with either of those positions, as long as we recognize that both of them introduce their own brand of bias into events around the D&D table.