For me the Manager/Head Coach is but one issue amongst several that need to be addressed regarding how the club is run.
The likes of Nagelsmann, Ten Hag, Potter and all these modern coaches are mostly working at clubs that let them get on with their coaching work and have structures and other people in place to help run the club and work to a strategy. Install any of them to our rather meandering and stale set up, with little help, and I don't have great hopes.
Levy has had a vision of how to grow the club off the pitch, and initially helped the team take considerable steps forward with the buy young talent who will grow with the team, and can usually be sold at profit in any scenario, but I don't see an idea or vision at the moment which is reflecting on some of the decisions made in recent times. There's a vacuum of ideas and people, we have Levy, Mourinho, who else? Steve Hitchen was an apparently fairly competent career scout, but as a DOF? Hardly comes across as a force of personality buzzing with ideas and a clear direction to what he's doing, does he...
On the footballing side we need a clear consistent vision of what we're doing, and under what parameters, maybe a bit of ambition and radicalism, and proper leadership.
No more going from high press, front foot, possession Poch who likes young malleable players, to low block, low risk, counter attack Jose who needs ready made disciplined seasoned pro's.
No more players signing who are ill suited to how we want to play. No more seemingly random signings because they share the managers agent. No more scattergun approach that means we're overstocked in some areas, whilst painfully thin in others. No signing players for big money, and not even knowing what position we want to play them in.
Personally I think we need a DOF/Sporting Director first and foremost to run and oversee the whole of the footballing side.
We need a proper scouting and transfer network/policy with clear vision of who and what we want.
I'd like to see us make a change in our Academy now (did we ever replace McDermott?), because the last few years seems to be repeat problems of a logjam, players getting stuck in limbo, and rarely producing the type of player the first team wants.
And when all that is in place, appoint the coach you want, based on the criteria we're looking, and hopefully he and the team has a chance of doing something.