As for your picks, all great managers obviously but as I said previously, one can pick holes in everything. Wenger barely managed a CL final, his European record is truly average and at times abysmal. I am not even talking about the time when he had no money after the new stadium, I am talking about when his team were dominating domestically. Look at their record in the late '90s and early '00s and let's not forget that in those years, the likes of Leeds, Deportivo, Monaco and Porto were making it to the latter stages. I am a big fan of Wenger and think his work at Arsenal is extraordinary in a very different way to the other top managers though, but to elevate him above the others is just illogical.
We can also criticize Klopp for how often he is the bridesmaid. Also, just like we can ask questions of Pep not proving it with a lower club, how can we know if Klopp can handle a club that is under pressure to win immediately like Bayern or Barcelona? How is he proven when it comes to managing the elite talent from the get go? He never had to deal with that in his career. Again, I think Klopp is one of the best PL managers ever but we can always find a question mark and asterisk. As for Mourinho, obviously one of the greatest ever but where do we start? How many things can you point at the man that others do not lack?
In short, all the names you mentioned happen to be good at different things and lacking in different managerial aspects. I think they all belong to the greats and depending on the context and what we are trying to evaluate, they all have a claim. But to make things simple, trophies and sustained title challenges married with pro active dominant football will always be remembered most which is why Sir Alex and Pep stand above all at this point in time.