Noone's saying that Arteta should be manager for life, or that he doesn't have his flaws. But in terms of sticking with him for the time being, its a no brainer.
First - are we progressing as a team under him? Undoubtedly. I'll accept that if we'd had another end of the season like last year this could be questioned, but we haven't. Our team has shown a lot more resiliance at the sharp end of the season whatever happens and our results against our direct competitors for the league, and our traditionally strongest local deby opponents has been better than anyone else's. Plus our stats in both attack and defence are the best in the league. If we get pipped to the title by a monster team that has won the past 3 and 5 out of the last 6 league titles and is regarded as the world's best then we still deserve to be regarded as an elite team.
Our first CL quarter final since 2010, and a narrow 1 goal defeat to bayern also clearly speaks to progress.
Second - will we progress further under Arteta? The signs are good. He is clearly learning and developing as a manager, and the speed at which our team is evolving past recent key players - eg Jesus; Zinchenko; Partey; Ramsdale is self-evident. His decision making re our latest player purchases , and ability to persuade our best players to re-sign for the club (along with Edu) has been excellent and our mostly young team hads not reached its ceiling.
Third - is there anyone else available who is better/likely to out perform Arteta at the present time? I would say no. This is of course partly because we are in the middle of his evolving project, but when you look at the names being mentioned for Liverpool; Manure - I don't think we can better our manager.
Obviously things eveolve and potentially can change, but I am optimistic going into next season, however this one now ends.