#1 Alternate route to Europe

Most clubs in the league would consider getting the chance to play in European competition a huge lift to their supporters and the club's image worldwide. European competition provides an amazing opportunity, attracting players that were otherwise inaccessible to them.
Birmingham City could actually take part in the Europa League Qualifying round despite relegation. While they failed to enter the group stage, other clubs could benefit from the European adventure more substantially.
Entering the group stages of Europe guarantees revenue increases from broadcasters, international exposure and an unforgettable experience for the fans.
The winner of the EFL Cup might have to begin the season early, but it is still a chance to earn European qualification in just 16 games spread over a year - 10 games in the EFL Cup and 6 games of qualifying. So much lesser than the consistency required to last a league campaign.
Winning the trophy also helps the club build up their bases for an ambitious launch pad for the future. It allows potential signings to be lured by clubs, making them an attractive option because of the success they have had by winning a trophy.
For instance, Swansea were able to consolidate their Premier League campaign thoroughly after their EFL Cup win. Despite struggling the next season. Micheal Laudrup was linked to many high-profile jobs because he had led a relatively small club to a major title.
So, an EFL Cup win certainly raises the profile of both club and manager.