Yeah, I think it's cultural, too -- a combination of a shameful physical self-image and homophobia.
I also meant to post earlier that, while a locker room is a public space, separate shower cubicles -- especially with a door or curtain -- are very private in comparison. The management just doesn't want anything funny going on, so they decided on a blanket rule to now allow sharing showers (easier to enforce, too, since the attendant wouldn't have to make judgment calls right there & then).
About the guys taking ten minutes in there --
What they need is a drill instructor to take charge. "Soap up your armpits right now! 10, 9, 8, 7,6,54321 STOP! Rinse them off right now! 10,9,8,..." etc etc.. Bingo, fully showered in less than two minutes.