I think you read the first line of my post and went of on your little rant, because you never touched on any of the issues I highlighted at all.
I'm not saying that I only want a British manager because they are so much better at managing than other nationalities, but the fact is that United are a British club, who play a very very British style of football. I for one would hate to see the philosophy of football here change, just because some Johnny come lately comes in with all the tactical bullshit that we know plays such a huge role in so many Leagues around Europe. United have always had the idea that if you score 2 we'll score 3, and that is what has drawn then support from around the world.
Also on my point about bringing in young British and Irish players and giving them every chance. Do you really believe that a foreign manager will give 1 shit about that tradition. Look at Wenger and see how many British players he has brought through. You mightn't think this is important, but for a team like man utd not to have any of its first team players coming from manchester would be sacrilege. IMO a british/irish manager would care more about this.
As to the part in bold, yes, I apologize for not addressing the other points of the post, but the bulk of the question is my disagreement with the idea that that hypothetical "tradition" will have any kind of measurable impact on the decision to hire a new manager. The only tangible advantage a British manager would have above a continental one would be a greater knowledge of the Premier League and it's culture, but that advantage is not a factor when the continental manager is Mourinho.
Now what I will say next may have some errors or omissions because I'm not a United fan, most of what I know about United comes from what I read on the forums or the few games of United I watch each season on TV.
It seems to me that while not as blatant in United as it is on Arsenal or Chelsea that tradition of bringing up young British talent at United is not actual any more. Who are the relevant British players at United at the moment? Legends from an ageing generation, or strong players bought from other English teams, like Carrick, Rooney or Ferdinand. Sure I see some mentioning here and there of guys like Gibson and Cleverley but from what I've been seeing lately the first is not so much of a talent and Bebé or Obertan are quicker called upon than Cleverley... Your academy seems to be more and more aggressive on poaching international talents sooner and sooner so that United can comply with the home grown rule without having to resort to the mediocre English talent.
Let's face it, English talent, proportion wise to the size of the country and the impact of football on the society, is not nowhere near good enough as it should be. Whatever tradition you seem to find at United regarding British players seems to be on a very fast decline, and so it shall continue to be if United wants to keep being a top European side. Until you sort out whatever problem formation football has at England, that's the way it will be.
Mourinho never seemed to have anything against English players while at Chelsea, he always used the good ones he had at his disposition. But on lack of better options he went for international ones, and that's how any future manager at United, be him whoever he is, will have to do to maintain the team competitive.