Klopp got to the Europa League final in his very first season. Arteta won the FA Cup in his first season.
There's a little bit of revisionism in that comparison, imo. Even Poch got to the LC final in his first season. In all their cases, there was enough consistent upward momentum that you could see the direction of travel - i.e, they got better each year/season, albeit with caveats (Arteta going 8th -> 8th for a year).
In Postecoglou's case, yes we had that same forward momentum for the first ten games. But after that, it was a concerning collapse that seems to have continued into this season. And of course, our cup performances were laughable last year so he doesn't have that to fall back on unlike Klopp/Arteta/Poch.
Just saying, more complex than that comparison lets on.