So you're defining a target man as someone who get's the ball mainly in the air. An old-fashioned English centre forward.
Therein lies the problem. Old Fasihioned. It is not current. That sort of football is not succesful anymore which is why that sort of player has been phased out.
You need to update your idea of what a target man is otherwise, as I suspect you want, this arguement will go round and round. Football has changed and old principals are no longer valid, thusly your position is not valid as the position of target man you refer to is no longer part of the game.
When I said 'target men are a thing of the past' I was referring to my understanding of the definition. ie the conventional idea of a striker principally used as a target for long, high balls.
This type of player, imo is extinct at the top levels of the game. And this is what I primarily see Carroll as, which is why I made the assertion in this thread in the first place.