Okay, shoot me.
I think it might be a modern solution to an antique problem. In the heyday of handkerchiefs you could do whatever you pleased with them, but today, wearing pants and socks out of doors is considered foppish and avant-garde. In that context, almost any expression of a handkerchief is going to seem affected and ridiculous. This is why many have abandoned them with sport coats, thinking the jacket pleasing enough. I see this fold as a way of sublimating some of the inherent goofiness and flair of the handkerchief by keeping it to a minimum ovoid form -- i.e., the opposite of a pimp-style pointed fold.