I don’t know about other leagues, but France had 2 domestic Cups. The League Cup was played for 26 years until the pandemic ended it.
There was a guy from Scotland on One of the old boards who took umbrage to any suggestion that the League Cup be discontinued. IIRC, his point was that it was a financial windfall for the lower level teams when the big boys came calling. But if the Prem is splashing more of their TV money to the EFL, maybe the time has come to end it. Leagues One and Two play for the EFL Trophy, so they have 3 cup competitions and a 46 match league schedule to contend with.