I dunno about the helmet but Air Force Cadets normally do their flying training in flight suits. Funnily enough, so did the RAAF when they were using CT-4s and I think they still do now during BFS at Tamworth.
One of the good reasons is that it is fire resistant. Our bloke in charge of AAFC flying ops in NSW is a bit of a fan of flying gloves as well for the same reason. I haven't work a flying suit for years (about '97 from memory) but found them comfortable, workable and they had enough pockets to carry EVERYTHING!