OTB tights are virtually never seen in our area. It's an area by area thing. But, that's off topic ... I actually just realized after reading your post that I've not really seen a pair in a few years!
The skater in question has a vulnerable area that the coach is attempting to protect. High level skaters generally are trained to/experienced enough to fall effectively (barring freak falls) which limits the need for protection; pads are really only for injury recovery or for learning something that is causing successive falls. We haul them out when we know that a jump is likely to result in a high level of falls on a hip or a knee, or the tailbone (or if there's an injury being nursed); otherwise, they stay in the bag as, regardless of how thin or light they are (we use Skating Safe) - they do restrict movement to a certain degree.