I wouldn't fume if we appointed Dyche, but I do have reservations about him. He has done a truly excellent job on a budget at Burnley. However, he is still a very British manager. I don't mean that in the sense of an Allardyce, Pulis, route one up and at 'em approach, I mean that in terms of his recruitment and outlook.
Look at Burnley's current squad -
https://www.burnleyfootballclub.com/teams/first-team/
What do you notice about the make-up of that squad? What do the players all look like? Where are they from? Of those that are not British or Irish you have:
Pieters - Dutch, signed from Stoke
Gudmundsson - Icelandic, came from Charlton
Wood - Kiwi, signed from Leeds
Vydra - Czech, signed from Derby
Whilst Brands is hopefully now the one with final say on transfers, or at least on a committee that needs consent to sign players, Dyche appears to only scout and recruit native English speakers or those from countries where most speak excellent English, and even then, he only signs players who have already played in England for a prolonged period. I will ignore the racial make-up of nearly every Burnley squad he's ever had, because I've never heard or read anything that would suggest he has a racist bone in his body, but it does concern me, probably wrongly though.
My overriding point is that I don't think he knows, or even tries to learn, about any leagues outside of England and Scotland. Recruiting only from these isles is much more expensive, much trickier and suggests an inability, or unwillingness, to work with players from different cultures, or who need to learn a new language. How do we think Dyche would manager, for example, Kean, Richarlison or even Mina?
His "my way or the high way" routine works at somewhere like Burnley with a tight budget and homogeneous squad, where he has proved himself successful in making them punch above their weight. If he came to us though, with heightened (realistic or not) expectations, bigger budgets and a very diverse squad including players on massive wages and with big transfer fees, could he really get the best out of them and implement his methods in the same way? I fear he could just be like Moyes at Man Utd only on a smaller scale.