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.
I think it is quite easy to determine what is the main priority, because logically they play in 2 big competitions, namely the English League and the Champions League. I am sure they will make both of them a priority to achieve the achievement they have been pursuing all this time. The English League is a more regular league, there are matches every week, so they have to prepare as well as possible. Meanwhile, in the Champions League, they have time to prepare, although perhaps at the start they will also have a busy schedule, because usually there are only 6 matches in the initial phase, but now they have 8 matches with the change in the Champions League format.
Actually, this is what worries me, in the midst of a busy schedule there will usually be problems, one of which is fatigue experienced by the players, and what is even worse is the storm of injuries that could come to them. So amidst the priorities they set, they also have to be clever in maintaining the health of the players.