You're confused again. Its not about being deeper, its about being expected to track runners from midfield and defend the space around the edge of the box. Carrick has all that expectation on him, or Blind when he plays. Schweinsteiger has always done the job in a 2 when playing as a cm. He's had help and usually from someone more suited to it than he is
Man, you tell me that I'm confused but it seems that unlike me at no point you seem to consider that we might slightly change the organization of the midfield.
By using a defensive box to box like Schneiderlin, you divide the defensive tasks between him and Carrick or Schweinsteiger, that's what I have in mind, nothing else, at no point I consider that we will just put the new players in the 'old' players roles without any tweaks.
If that makes me confused then fair enough, I'm confused.
Edit:
I understand that you see Carrick as our first wall infront of the defense and you consider that Schneiderlin is very potent defensively and could shield the defense like Carrick does, and you are right.
But I see something else, we have Schweinsteiger one of the best deep lying playmaker in the world, he isn't as good defensively as Carrick but he shares a lot more of things with him than Schneiderlin does, they are both great at controlling and orienting the game, they both have a great passing range and they are both good at anticipating the game.
Schneiderlin is an all action player, he doesn't have the passing range, the positioning or the tactical leadership of Carrick, but he is mobile, athletic, comfortable in tight space, aggressive and run well with the ball, on top of being very sound defensively.
Playing Schneiderlin as a box to box, allow you to use all his attributes at once but also compensate Schweinsteiger 'deficiencies' by giving him a defensive support.
In my opinion if you use them the other way around you limit both players.