The fact that girls are permitted does not preclude the need for boys to gang. The same is true of girls.
When we think of patrols or cooking groups, it seems likely that they might be gender segregated simply because that is what the kids want.
In Scout units where girls 14 and older are permitted, there are many years ( at least 35) and lots and lots of very positive experience. There never have been a lot of girls, but there are many that desire participating in the rigorous scouting outdoor, advancement and leadership experience. That experience includes backpacking on a 70 mile trek at Philmont or sailing th Bhamas from Seabase.
I argue that you are simply wrong.
I am not going down your rabbit hole. The dynamics of the gang is that which is at stake. Ignore that for some sensibility of equality is asinine. If you believe that men and women are the same, then you are right. However; men and women are different on so many levels. We are wired differently. This is not opinion. This is backed by scientific data. Our brain function differently; males have less nerve sensitive; dealing with emotions are different; we learn differently; ETC. It is bad enough that boys are getting shortchanged in our wonderful educational system. One of the few places where proper male development can occur, is being adulterated by progressive claptrap of universal inclusivity.
Ask yourself why has the Scouting program been so successful. How did it start? What was the original Scout handbook? Was it developed from a co-ed classroom or the field? When you remove a pillar, then the hall is weakened.
I agree with UpInArms. Your entire argument seems based upon the premises that the psychological needs of boys and girls are the same, and if not, then the presence of girls has negligible effect upon male socialization and character building, both of which are obviously false.