I find it hilarious how many people seem to just see Fellaini's name on the teamsheet and then dont even bother to watch the match, but rather just assume we spent 90 minutes hoofing the ball up pitch.
Having a physical presence and an aerial threat in the team is very valuable to diversify our attack. This doesnt mean playing hoofball, this means giving us options.
Look back at last year when we were swinging in crosses constantly and had nobody to get on the end of them. Having a physical presence up front forces the opponent to change the way they defend - they can no longer just sit back and allow the ball to come in (in the knowledge that they can outjump us), but rather they have to try to stop the ball coming in.
The above may seem like a small difference but can in fact be a complete game changer. If the opponent has to stop the ball coming in rather than just packing the middle and basically force us to cross it (because all other avenues are cut off) then the gameplan changes. We have seen it a few times this season when this has been the case, and by forcing the opponent to defend wider areas it actually opens up space in the middle for us to attack and exploit.
To put this another way - had Mata played last night instead of Fellaini, here is what I think would have happened (roughly);
We would get the ball, Arsenal would defend the middle of the pitch, denying Mata and co. any space to work with. They would thus inevitably have to send the ball out wide to Young and ADM, who would be forced to cross the ball because they have no other option. They cross the ball in, and Mertesacker has a right old laugh as he comfortably deals with it. Repeat for 90 minutes.
Having that physical presence who can challenge opposing CBs is a vital factor for us at the moment. Until we have players like Silva, Aguero, Hazard, Coutinho, Sterling etc who are capable of beating a man or unlocking a defense, or just scoring a cracker from range. We have none of that on a consistent basis.