At the T&T meets my daughter goes to its very common, might even be more common for the athletes to wear shorts while competing. So I'd say giving kids the choice to cover up more may be better received than you think.
I think a lot of the college girls are unfortunately buying into misogyny, that showing skin sells. They can make money on their image now, and scores often reflect audience participation. So unfortunately, probably without even knowing why, they prefer to show more and hike up their leotard. The college gymnasts I know are often given a competitive leotard 1 or even 2 sizes too small. So those girls aren't given a choice on showing more skin. That leotard will not lend itself to coverage. On the other hand in college these girls are adults, so if they want to wear the less modestly cut leotards that's their prerogative. I just wish college's would give the girls a shorts choice too. Sociologically, I wonder if, or how long it would take for the girls to shift their behavior?
My daughter once did a private to fix her vault. It was amazing how quickly her score improved after she had some one on one time to fix her run, her steps, and her jump to the spring board. Her score went up a whole point the next meet. It was very beneficial. We tried other privates few times after that with only limited success. But that one private was amazing. As a whole though, her gym didn't suggest private lessons to the athletes or their parents. If they weren't getting it at regular practice then they either weren't practicing hard enough or they just weren't ready for it yet.
I think gymnasts at all levels should get an extended time off every year. Like a month in the summer. I think it's good for the body and soul.