And what category did Manuel Pellegrini fall into when he was appointed by the exact same individuals appointing our next manager? Is Manuel a serial winner or influencer? I would guess neither.
So what is your point with regards our next appointment?
correct. pellegrini is not a top class manager. the team that pep inherited from him were an absolute mess.
the reason why so many top class sides (real madrid, bayern munich, chelsea, arsenal, manchester united) are now turning to ex-players, is because they've worked out that just because someone's done a really good job overachieving at villarreal/malaga (or everton, or southampton/tottenham, or swansea/leicester), that's not usually reliable evidence that they'll succeed at a top class side, because the challenges are very different and expectations are a lot higher.
so the owners/directors of football are instead taking a punt on fan-favourites. someone who at least has a meaningful connection to the club, and who understands the club's culture.
there's no easy answer to your question. i'd love to see bielsa manage us, but i accept it's unlikely. ideally vieira or kompany would have taken the assistant's job and had a few years under pep's tutelage. but unfortunately those are both out the window as well.
given the options available to us
1) pep manages us until he dies
2) arteta's made a good start at arsenal, and i'd be monitoring his progress next season
3) lillo would be a decent option, in terms of replicating pep's style
4) if we can't appoint someone with direct insight into pep's methods, i guess we'd have to settle for a pochettino type appointment, though provisionally i'd prefer tuchel (given he'll have title-winning experience at psg) or nagelsmann (given he's ridiculously young to have coached in the champions league)
having said all that, i don't actually think pochettino would be a bad appointment. but we'd very clearly be appointing him based on his potential to become a top class manager, rather than on his current status as a top class manager.
because if you go your whole managerial career without winning anything, and without influencing another manager who wins things, you absolutely cannot be considered a top class manager.