In my dealing with helmets for various applications tells me most mandates also require a current safety standard rating on the helmet. I can't just jump on a motorcycle in Michigan, for example, and toss an old WWI German helmet on to comply with the law, it has to be marked as DOT approved. According to Wiki, you require something that adheres to AS/NZS 2063.

Whether or not you expect to get checked on that, I dunno, but worth keeping in mind. As a personal matter, I wear a current (albeit cheap) helmet, not out of compulsion or worry about safety, but because it is much more comfortable than a ball cap or my hair flopping everywhere on a long ride on a hot day.