For the reasons you've stated about his all round game, I doubt many people would, hand on heart, say he's world class.
Mind you, he's slowly improving his all round game so you never know.
Given he'll probably score 20 goals or so this season I guess the question is, which would you rather have, a Rom goal scoring machine or someone who's got a better all round game but might only score a dozen or so goals a season ?
Personally I'd stick with Rom and find a player, or players to complement what he does.
The other guy.
Because what happens right now, as we saw yesterday, is that when Rom doesn't score, he's in effect useless.
A better all round striker brings the whole team further up the field and innovates the entire attack. Goals come from different angles. Right now, we're easily nullified and seem to only score and win when Lukaku gets something out of nothing, and you can't coherently strategise for a run of games on the spin with a plan of no more than simply crossing your fingers and hoping Lukaku turns up.
You know what would be more ideal though? Lukaku and a striker who can do the legwork - a second striker to link things up whilst Lukaku hangs on the line. If that means dropping Barkley, so be it, because Barkley would work better with an all round striker who can get him further up the pitch and attack from deep.
But what I do know for certain is that having Lukaku the way we do now simply does not work with Barkley behind him. Neither player is actually to blame; it's the system.