I don't think he's as great as a winger & I fully understand why he's not interested in playing there. Defensive responsibilties, restriction of movement to one side of the pitch, playing wide means he has to play on the touchline outside the box.
Defenders usher him wider, he's not really a crosser of the ball
It just completely inhibits his game, to where people for instance think he can't pass.
Sturridge is great in the box, he loves to play on the channels to use his pace, but, crucially doesn't want to be restricted there. Obviously down the middle as well on the shoulders of the defender he uses his electric pace to great effect on the counter when he is central.
He drops deep & finds teammates well, he likes to slow dribble across the park
His game just becomes so much more 3D when played as a striker.