It's one thing to stay back (which Carrick will do). It's a totally different thing to have the defensive positioning and know-how to either slow the attacking team down enough for your other midfielders to get back, or to force the attacking team to one side with no real chance to cut it back inside. Carrick doesn't have the ability to do this regularly against teams who thrust forward fast and with purpose.
If deep-lying playmakers are good enough to be used as the main holding midfielder simply because of the fact they sit deep, why do Milan waste a spot on Gattuso when Pirlo could do the job? Why did Benitez sign Sissoko when Alonso is more than enough? Why has Vieira gone through four different defensive midfielders at two different clubs (Petit, Edu, Gilberto and Emerson) when he could do it all himself (I don't think anybody would dispute that he's better defensively than Carrick). Why did Real Madrid suddenly implode when they sold Makelele? Why do every top team in the world use a holding midfielder?
Using a defensive midfielder doesn't make you a defensive team. Used the right way it allows your other players to concentrate more on their attacking duties. Barca, Arsenal, Lyon - they all use them and are probably the three most attractive attacking teams in the world at the moment. In fact, they all play a defensive midfielder next to an all-round midfielder, which according to some would make us a boring team with not enough goals from the centre of midfield. Those three are prime examples of how it should work - not the defensive versions that Chelsea, Liverpool and the Italians use.
I think it's Mozza who keeps throwing out the line about us never having played with wingers who ignore their defensive duties. Nobody ever said anything about completely ignoring them; it's simply that with a proper defensive midfielder behind them they won't have to do as much defensive work as they will with a combo of Carrick-Scholes, which therefore allows them to be in better position and more of an attacking threat on a consistent basis.