Are you still not aware that none of the managers in the PL are arsed about the league cup? Where have you been hiding since the authorities had to make the league cup compulsory for all league clubs when a good few in the PL made it plain they did not want it? Clubs with any ambition are (were) content with league. Fa cup and where possible Europe.
As someone else has already said, if a club somehow drifts into the last eight by selecting under strength teams without seriously affecting their first choice players, and their league/Europe involvement, only then do they start to get interested.