Draven is on screen, he is a speaking role, as is Raddus. We hear Mon and Bail talking about having to confer with Raddus in a context that iirc outright mentions he is with the fleet. The Alliance is not really shown to be completely run by the senators, though yes they are the main figures we get full conversations/arguments with. I am just saying, these other elements are literally on screen and spoken aloud.

https://www.youtube.com/watch?v=9u3GGIQrOdA

Raddus is shown to be in a position of power, he gets the line that they don't have a quorum which confirms more leaders not there, then the line "Dodonna and Merrick(who a prior line tells the audience is a military hardass who would've shot Cassian out of the sky) will be back tomorrow" and only THEN can a full session occur.

So the show does, textually come out and say that the senators don't have power over these matters, and that approval, while given off-screen, comes AFTER these military figures are back involved. Mon and Bail are focused on cause we had time to know them already, but the show does not make them singularly important to Alliance leadership.

Whatever else is wrong with the Alliance politically, it is not being run as a fighting force by comfortable politicians, the show makes that explicit.