As mentioned you have the size of the squad incorrect, and you don't have to play them both together unless the occasion suits or even play them consistently as starters. We also don't have a CM in our entire squad currently who can bring to the table what an on form Carrrick can and as yesterdays showed he is still not finished as a premiership player yet.
As for Bastian I feel that some have written him off too soon as well as I still think he is getting used to the prem and will be better for his troubles this season as he looks a little off the pace(as have most of our players on random occasions so this may be a coaching and management issue). The fact is having a player of Bastian's experience even if it is only in the dressing room is a God send when it comes to bring through younger players.
That type of experience and professionalism is something you cannot easily replace so it would a silly decision to get rid of him simply because he cannot start up to 60 games a season anymore.
I haven't got the match day squad wrong, it's 18 players, do you really see them both sitting on the bench and accepting it? I highly doubt it, and you don't need two of them there, only one to come in late as a 3rd CM. Carrick had a good game yesterday against a 1 man midfield, most of his games this season he's looked like a statue and unable to keep up with the pace, keeping him is more of the same treading water that got us in the mess we are in, we should replace players with top quality when they start declining heavily which Carrick has, instead of keeping them until the wheels completely fall off.
You want to keep the experience then put Carrick on the coaching staff, he can add it from there and leave Scwheinsteiger to be the guy that comes off the bench in games when we are looking to close out a game. Keeping both means we'd almost certainly have one of them starting games most of the time and that's not good for this teams chances of progressing.