I have been a fan of Carroll's for a long time now (as anyone who can be bothered to trawl through my post history will find out.) I was disappointed that he didn't get a run in the first team earlier.
The thing that I like about Carroll is that he is able to move the ball forwards quickly, often one touch, and has a good eye for forward runs, often passing through channels into space for people to run onto. He also looks for quick one-twos. He is a tidy player, and has a lot of energy. And he can shoot Ok too. The ability to make quick, incisive forward passes is a very valuable commodity in the modern game. The pass won't always come off, but it is likely to lead to some of the few chances that we will get in a game.
I don't worry about his lack of physicality too much. Providing you have the vision and technique you are more likely to end up being fouled after you have moved the ball on than be a liability due to lack of tackling. And as the stats show it is more about pressuring, nicking semi-loose ball, covering and tracking back these days than the balls-out, take the ball, man and everything within 15 yards, tackling of the 70s.
Carroll is far from the finished article or the complete player. He will get out-muscled at times, and he could do with being a bit quicker. Overall, though, I think his positives far outweigh his negatives. He will benefit from a regular run out. His team mates will learn to trust him with ball even when tightly marked - not something that I'm sure all of them do at the moment, as he doesn't always get the easy pass to feet even though he is demanding it. He will build a rapport with the other players.
I don't think we should turn this into a Carroll vs Mason vs Dembele zero sum game, as they have different playing styles and each offers something different. No doubt, there will be games where each of them has an important contribution to make.