I jave traveled several times domestic and overseas with zero protection except for a strap that goes around the Brommie and holds it well together. No damage. I think a semi-soft bag is more dangerous that nothing at all. The one time I had my Brommie in a soft bag, also with the same strap and additional padding and so on, the steering got bent.
Was your bike checked or carry on? If checked, I've wondered if the lack of case - so that the handlers can actually see what it is - means that the bike would be treated more carefully.