I've actually had ballet teachers tell kids that it is unhealthy/unsanitary to wear regular underwear under tights because of the way they gather and hold sweat in that area- that over years of teaching they see the kids who wear underwear get yicky "girl infections" much more frequently. Those who just wear their tights don't have the same problems.
I've heard others say that cotton crotch means no undies needed. I think it is to provide ventilation to prevent what you've described, not replace panties. The kids and I wear cotton undies and have no such problems, but I guess skaters wearing nylon panties would be prone to what you've described. Then again, the nylon undies could be the real cause, and it's been attributed to all panties without any real scientific analysis, lol. Who knows?
I hate wearing pantyhose or tights without underwear. I always feel naked and uncomfortable. The chafing that results from the legs stretching and pulling the crotch is literally a PITA (or thereabouts.)
The other reason to wear panties under tights/pantyhose is because of unexpected menses - I had three skaters get their periods unexpectedly at competitions and tests this year. Since the Synchro skaters' dresses are held for them, that means an embarrassing conversation for the kids with the costume manager.
To each his own, but the cotton crotch provides minimal modesty coverage, which is wrong in a sport where we require them to haul their foot up over their heads. I like short-shorts...and I don't think we should dictate underwear requirements for skaters of any age!
A coworker was once given a comment by a much older man at our office. He remarked that she was wearing pants to work. It was a designer business suit from Saks, very appropriate for work! Under her breath, she muttered to me "If he wasn't looking at my ***, he wouldn't have noticed." lol
If you start them out young, they won't think it's weird at all, they'll just be used to it. That's the reason to have 5-year olds the same as older kids. The problem is when you tell an 8-year old she can't wear underwear. Then she thinks your crazy.
That drives home the point that it's inappropriate to ask them to go without underwear at any age. Just because we brainwash them by "starting early" doesn't make it right. An eight year isn't even as self-conscious as a 13-year old, so they don't think you're crazy, they think you're creepy.