I've been reading up a lot about what happened at Arsenal, and I think it tells you why (PSG aside), Unai has preferred to go to teams with potential, but which are lower in the league. It seems to me to be entirely about players mentality.
Players under him seem to respond in one of two ways to his leadership. You either buy into the micro management, or you reject it. At Arsenal, by all accounts he had players openly mocking it. Big egos who didn't react well to being told exactly where to go and what to do. Whilst I understand it to some degree, it's important for the players to understand that he doesn't do it because he does not trust them, he does it because he's building a functioning machine, where each part is important.
Players who he's managed tend either to hate him or love him (Guendouzi in particular says incredibly positive things about him), and form strong bonds.
For this reason I am now thinking that even with the War Chest (TM) , we'll be very selective in recruitment, and it will be more focused on mentality than individual skill.