I've never really been one for claiming a certain "type" of footballer has no place at Anfield, so I'm not sure wondering how he'd "fit in" was all that valid when we signed him. Certainly, Rodgers must have had some clue to persuade the club to spend £32m on him, and I've been at Anfield watching him play for Villa, when he totally decimated us. And there didn't seem to be a style of play evident, he was just great; powerful, quick, great finishing and also really good with the ball (seem to recall a cute back heel to set up a goal too).
Same with Carroll. With him Kenny did try and bring in players who could supply the sort of deliveries he would thrive on, but his lack of fitness, effort and mentality seemed to count against him. And he wasn't helped by the likes of Downing and Adam being ever so slightly underwhelming.
I do have a preference for pace, beautiful finishing skills, lovely technique etc; watching aesthetically pleasing strikers like Fowler, Torres, Suarez and Owen scoring with brilliant abandon is joyous. But I'm not 100% averse to having a slightly less artistic striking presence, as long as it's effective and they score goals.
Look at Giroud. I'm sure most Arsenal fans wish he was Thierry Henry, and prefer Sanchez, but they've had great service from him, and he's a player with a pretty defined style and attributes. They just maximise them. And nobody moans about them changing to a more agricultural style, or lumping endless high balls into the box.