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.