I've noticed that too. My guess was to minimize wind resistance. Heck, locally I see pros from the Elevate team training in that second-skin kit.
I'd be tempted to train in more traditional looser fitting gear to gain the at least psychological advantage of feeling more aero in competition.
My handlebar tape is an old tube cut into strips. Helps reduce chatter and vibration with minimal added thickness. But it's slippery with sweaty hands so I wear gloves. I need to add some regular bar tape over it. Got some in a box ready to go. Been saying that for months. Some day it'll come true.