What a brilliant trend :) The truth is, hats are far less of a bother than people think they are. Like you said, all the fussing comes when you're on the ground - once you're on the horse, who has time to worry about their clothing or hat unless it's giving them pain? It's one of the reasons why I use physical activity to relax: you absolutely have to disengage your mind from whatever you're worrying about and focus utterly on the horse.
When it comes to the strap ... it is a tiny bit safer to have a loose strap than a loose helmet, but obviously both ought to be snug. You could just leave it unclipped while you're on the ground so it doesn't bother you there.