Arteta has proven enough that he is a good coach because this season he really brought Arsenal to the top. He indeed failed to bring Arsenal to the championship but that doesn't mean he's not capable of being Arsenal's coach. He should have known what made Arsenal fail, and that should be used as a lesson so that Arsenal can have more thorough preparations next season.
Arteta has really good players, but he's not good at rotating his players well so when a player is injured he can't get the right replacement, Arsenal needs a few more players to be able to fill the void and Arteta might be able to rotate players well if the composition of the players is quite complete, this season as usual he has to be satisfied with the final result that Manchester City is more worthy of winning the EPL title again this season, Arsenal's players don't have enough of a winning mentality so they haven't been able to show completely good results.
If only Arsenal had not failed against Aston Villa, maybe Arsenal would have become EPL champions this season, of course this defeat should also be an important lesson for Arsenal next season, don't focus too much on pursuing important rankings and positions in the standings at the start of the season, make sure the players remain be consistent and maintain their performance so that they remain in good condition until the end of the season, because Arsenal always make the same mistakes at the end of the season, therefore this must be an important lesson and not happen again next season.