Again, hyperbole. I am not particularly a Xhaka fanboy, but it does frustrate me that he is regarded as a fundamental problem, when the evidence suggests otherwise.
Every manager needs to prove themself. You are making a massive assumption that Arteta and Emery have sought to do so by backing 'teachers' pets' irrespective of their performances on the pitch, but this makes no sense. Sure, every manager will have a playing style that suits some players more than others - for instance I have sympathy with Pepe whom I think has real talent going forwards but has never looked a fit for Arteta's teams - but this doesn't speak to personal bias.
You talk about managerial gravitas, and by implication criticise Arteta for not having this. There have been planty of managers with so-called 'gravitas' who have not done particularly well in the EPL. What is more important IMO is that a manager gets his team playing well - and whatever your criticism of Arteta he is achieving this. Even more importantly at Arsenal there was a crying need to change the club's culture. Dropping a player who was consistently late or flouted club rules is key to this, and persevering with a player who has been sent off fewer times than his rep would have it (as I point out above) is not inconsistent with this. It depends on what other qualities make up the whole, and for all your criticism of our successive managers it is far more likely that Xhaka has qualities that are regarded as valuable to the team than that they have all kept faith with him simply for being a sychophant.