Mou was a nobody as a player as well. So was Tuchel. And Klopp. Do you really think world stars have more respect for a guy just because he was an ok footballer 30 years ago? I'd bet if you give Valverde the Chelsea job tomorrow most of the players wouldn't even know for what clubs he played.
There is more to being a good coach, more to being good at leading a team and getting respect than just the things you listed.
Disclaimer: I'm aware Barca is different. I wouldn't sign Sarri. It was just a joke.
It doesn't mean that you NEED to be a former footballer, but still...
Imagine these coaches in the next season:
Ronaldinho, Puyol, Henry or MTL Barca.
Do you think that kids like Dembele or Alena would respect/have more fear towards Ronaldinho or MTL Barca as a coach?
Further, even if you were not a footballer, then you need to have results in your career, and some leadership personality like Klopp or Mou.
It is hard to be a coach who is not a former famous footballer, mixed with being a quiet personality and without crazy results on his back.
Klopp and Mou have results, leadership personality and players have some fear and respect towards them, at least in early seasons.
Objectivelly, Sarri has only some needed skills.
But since he played a nice passing football, people here lost their heads.
Just like with Sampaoli, Jardim, Setien.
With players, people here are obssessed with: he is young, has potential and is passing the ball well as 3 key skills in football.
With coaches, people require only one thing: a coach needs to play a nice, attacking football.
I mean, there is nothing wrong with a nice football.
But for Barca's coaches, there are so many other things to be considered.
Imo, Van Bommel would break Kepa's legs after the match if he did the same thing in his team.
That's the difference between Klopp, Pep, Van Bommel and too nice guys, who are mentally not strong to lead the biggest clubs and deal with the internal affairs.
** Alex Ferguson threw a boot into Beckham's head once when he was causing internal problems, lol.
That's how you win trebles...