One of my hobbies is cycling time trials and I also cycle for pleasure and general fitness, in addition to the training. I've come off twice, not whilst racing and both times not wearing a helmet would have resulted in serious injury - one of the 'off's' resulted in me having to replace the helmet. My rule for me and my kids is 'no helemt - no ride - no discussion'.
To me it's nonsensical not to mitigate a risk where the means to mitigate it exist....
Sorry, I forgot the bit (reference the original question in the thread) about the bikes. I use a much upgraded 2002 Raleigh Special Products R300 framed road bike for time trials and road use and a German tank made by Pegasus for the other stuff. Once in a while I'm let loose on my son's homebuild (mountain bike) based on a Marin East Peak frame, but because last time I tried to show him a trick and made a complete a*** of myself, he's reluctant to let the old man loose on it now and risk it getting damaged again.