I would restructure both the lower league competitions for two reasons.
Firstly, they are too much of a distraction to the higher placed teams; resulting in dismissive team selections that end up showing disrespect for both the opposition and the competitions.
Secondly, there are, currently, too many matches being played during a long season. This results in too many mid-week matches early in the season and a congested programme in winter where travelling can be made hazardous by bad weather, attendances can be hit by both the weather and by Christmas commitments and the pitches can suffer. The latter impacts the lower (and less affluent), clubs more critically then it does the better off.
To mitigate these problems I would (a) dispense with the EFL trophy altogether. The inclusion of EPL U21 teams has not had any positive impact that I can see. Also, the one benefit that does come to mind - that of providing competitive game time to peripheral squad players, can be catered for by (b), restructuring the EFL Cup.
The EFL Cup should be competed by EFL clubs in the Championship, Leagues 1 and 2 and by all teams in the Vanarama National League. The Cup would not be open to teams in the EPL.