Likee I said in few other occasions, his role should be Gattusso's: main asset is offset a deep player soft attributes and breaking play and everything else is average. Occasional exceptional thing he does is a bonus, not standard and to be expected. Simply put the very raw definition of destroyer than defensive midfielder.
Compare to Makelele type: Schneiderlin is much worse disciplinary, and positional and tactical sense. He often got sucked into action at the wrong time and leave gap for opponent to exploit. That's only tlaking about role's duties, not players attributes, which for example Makelele is tougher and lazer quicker in breaking up play.
Compare to Kante type (very similar but still distinguishable): Kante is like pressing specialist, similar to Edgar Davids too. Pressing specialist in that they don't do anchoring role like Makelele or deep playmaking like Carrick, Alonso, Pirlo,... they run around offer energy mostly in defensive phase starting when losing the ball, but not doing as much in attacking phase.So why is the difference? It lies with Kante being afforded a independent role, while Schnederlin should babysitting the anchoring midfielder. Kante can go press as soon as the ball is lost while Gattusso's role is anticipating on anchoring midfielder. Kante despite his role receive very few yellow as far as I see from his 2 seasons in the PL since if the niggling foul is way farther upfield, it's more forgivable. Destroyer risks more by committing foul every where.
Compare to box to box, player like Vieira or Essien, Keane,... it's so easy since he doesn't offer enough all around both defensively and and offensively.
He should be bought to comply Carrick, but instead is wrongly used as Carrick replacement. Then being expected to change his game to comply Bastian who is different than Carrick (see my other post in Bastian thread)