I don't think it would be prudent for Arsenal to focus on only the premier league and not on the champions league. Arsenal is a big team and a big team fights for all the trophies available in the season. Focusing on one from the beginning of the season might be catastrophic because if they lose out on that one then they're left with nothing. Great importance should be placed on the major competitions which are the league and champions league. They can use the reserve team or second 11 to play competitions like the FA cup or caraboa cup if they're not facing a top opponents, but the champions league and League, should be their priority.
A team as Arsenal needs to choose their priority as soon as the season is starting so they can achieve one trophy this season as they have been going tropyless for some seasons. Other teams that has been having a bad season are getting crown champions in one tournament but arsenal is getting nothing and this is not looking good for the manager as it will put him under more pressure. Trophy help keep a manager career so he can impact the team and work with them to win bigger tournaments. Arsenal need to start winning trophies and if it needs them to focus on just few tournaments, they should do it.
What priority is this? I think, as a professional club, Arsenal must be working professionally. No league should get priority. Arsenal must prioritize all competitions. This is because winning trophies in all of professional scenes is very important. They must have strengthened their mentality. Working harder in all competitions raises your chance of winning.
And again, focusing only on one competition won't guarantee you to win it. Arsenal almost made it last season. But, City took the lead at the end. This surprised many people. And as you said above, having a bad season, but winning at least one trophy was better than being trophyless.
So, Arteta needs to fully concern himself with the mentality of Arsenal's players. Arsenal's performance is good so far. However, it lacks a trophy. This incomplete journey is a concern for Arteta, and his club must be focusing on all of tournaments.
I remind you: the team is not just playing for the trophy. They must also play for their finances. The trophy is not everything, but winning it helps you a lot. It boosts the reputation of your club. Then, you can sell your players for a high price.
All in all, Arsenal only need to improve how to win the trophy. This is it, a proper finishing, and that's very certain if it's the only aspect missed by Arteta's club.