I should clarify my position. No "personal protection equipment" is a substitute for being vigilant.

If a car hits you, yes your skull might be protected, but there's your neck, spine, limbs… all unprotected and equally as vital. It's a matter of risk assessment. If risks can be reduced easily, then it's worthwhile doing so in my book.

Maybe a solution is to wear the helmet short-term during the "hairy" bits of the run.

It would appear wherever you are, you have a choice. If you were riding where I was, and tried riding without a helmet, you'd be pulled over by the police and issued with a fine for not wearing one. So you'd just have to make do with your hairdo to suit being confined to a helmet for a hour or so over here — this discussion would be completely academic.

There are helmets out there that do protect the face, but not very common on the road. They tend to be worn by mountain-bike riders off-road.