This is rarely discussed now as Mourinho has went a full season without trying him holding midfield. Herrera has made that position his own and Carrick has signed on another year. Personally I feel it is his best position but Ander is better and Carrick is a very useful squad option. If we are talking hypothetically about moving to a midfield with one holding and two in front of him rather than a double pivot with an advanced midfielder in front of them, and using Herrera higher up the pitch rather than as the sitting player, then yes I would say Blind should be considered as a starter over Carrick. This is due more to the fact that he would be able to play a full season rather than actually being better than Carrick in the role though. I think Blind could play a full season in that position and be good enough for a team challenging for the league title.
His lack of athleticism is always going to go against him when discussing his suitability for any role, however I don't understand the opinion that he is too weak or too slow for centre midfield specifically? Anchoring the midfield is the best position to limit how much he gets exposed physically. Centre halves and full backs are far more likely to find themselves in need of pace or strength during games - particularly the amount of space you have to cover is greater. In centre midfield everything is more compressed, with supporting players all around you. Alonso, Carrick, Pirlo and an aged Scholes are all examples of players who's physical limitations were offset by their playing position. Carrick and Alonso, like Blind, have a greater aptitude for defending than the latter two did and although the complaint that they are not quite athletic enough has been and always will be the case and will show in certain moments of games, they are intelligent enough to not be a hindrance to their team defensively. Pirlo and Scholes at times were a liability, with no knack for positioning and no recovery pace to bail them out. They of course had a place in their sides in spite of this due to their obvious genius on the ball.
While Blind is not quite as good on the ball as any of the four players I've mentioned he is still extremely competent. As things stand, Herrera is our best holding midfielder. He developed rapidly in that position last year to the point where I would prefer we keep him there rather than move him positionally again. However, the one area where I feel Blind is marginally superior is circulating the ball progressively. Herrera infuses urgency into the play, but still very occasionally will receive the ball off a defender and zip it back when he could be on the half turn and play a more positive pass. Blind, like Carrick, always knows what's around him in possession and always picks the right passing option. He doesn't display the propensity to play long diagonal passes in the air like Pogba, nor drive a relatively long pass along the ground into a strikers feet like Carrick but he provides consistently forward thinking short passes.
Blind is a very intelligent and adaptable player as seen with his ability to fill in in several positions as needed. I would imagine that as a midfielder he could easy conform to whatever tactical instruction Mourinho gives in terms of team shape. Jose will oversee a myriad of subtle little changes to his side's setup from week to week to neutralise and exploit the particular shape, strengths and weaknesses of the opposition. Blind is the kind of player who would understand and be able to execute changes quickly in this regard.
That being said, Blind does have one big mental weakness in his game. He looks to anticipate passes and is very positive with his pressing when he identifies an opportunity to win the ball back. The majority of the time this is good and leads to good tackles and interceptions. However, occasionally when he pushes out to press or intercept he leaves an opposition player in a (more) dangerous position unmarked and risks taking himself out the game and leaving his teammates exposed. It has happened at centre midfield, left back and worst of all at centre back where he is essentially last man and there is no cover behind him. He needs to better identify when he should hold his position and keep the team balanced. I do think this is also somewhat mitigated playing in midfield as the defence is then still there to offer time for the team to recover.
Blind is a good player who is best as a holding midfielder where his strengths are amplified and weaknesses alleviated. We have a stronger player for that position in the squad right now and the only reason to play him over that player would be if we were freeing him up to play further forward. I like him but I certainly wouldn't want him doing a man marking job on Eden Hazard.