His top speed's adequate, but his acceleration really isn't, and I guess his size is part of that (although a player like Van Persie doesn't struggle in the acceleration department like Carroll does). Unfortunately it's those first 5-10 yards that Rodgers probably values because of his pressing game.
And honestly I can't imagine Carroll finishing particularly astutely. He just hits the ball with as much power as he can muster, which to be fair is quite a lot, but when it comes to sticking the ball anywhere with much precision he seems to struggle. There was that embarrassing moment when he won the penalty against Chelsea in the Carling Cup, had the stones to grab the ball and demand he take it, then fucking hoofs it straight down the middle with an emphasis on power, which the keeper stopped easily. Honestly the best way I'd describe Carroll in the box is like a defender, I don't see any innate ability to find the net like you would with most strikers. It never looks natural to him.
