Look this is a chicken and egg argument. Big Players want to play for big, successful clubs that compete in most prestigious tournaments and pay the highest wages.
Winning League Cups and FA cups does not make you a big successful club. It's a great day out and the fans including me, love it but it isnt about building sustainable success. Look at Arsenal they have won what 3 FA Cups between 2010-2020 and are still languishing below us in the league. So savvy managers will prioritise competitions that build long term success rather than short term glory.
@Raziel, Arteta won the FA cup last season, it won him lots of good will which then evaporated about 5 games into this season when it was clear that even with that win, Arsenal are no better in the league or cups than last season. No one fears Arsenal or seriously believes they are going to be competing for big trophies. People did take both Arsenal and Spurs seriously though when they were competing in the Champions League and finishing in the top 4.
It will not save Arteta from the sack imho and it will mean that he will be in post for less time than Poch despite being a "winner". The same will apply to Jose, despite his credentials, if he only wins the Carabao Cup and doesn't qualify for the champs league. It also worries me what our top players will think the longer we remain out of the Champions League. I would forego a win in the Carabao to win the Europa League tbh. I think all our eggs should be in that basket once we reach 40 points.