The FA Cup is fine on its own. We don’t need the EFL Cup too. Most clubs priorities the FA Cup way more, it’s a more prestigious prize and the tournament has way more fixtures. Clubs also prioritise league matches over the EFL Cup anyway, so the EFL just adds to the fixture congestion of a lot of teams. Players are getting injured across every team anyway.
During a busy fixture schedule, clubs have to put together a team to play in the EFL cup midweek whilst trying to save their best players for the important league match 3 days later, but also trying not to get humiliated too badly in a Cup game that most teams don’t really care too much about.
There is no guarantee that removing the League Cup will give players more rest days. The FA and TV companies will shoe-horn ways to include more fixtures.