I would personally not lock it to the bike as I don’t trust half of the people walking about. No doubt you will come back to it being scracthed and broken. I usually just carry it around with me, you can also get helmet bags though which I guess is more convenient.
Most people don’t realise how “fragile” helmets are (i.e. a good kick and you won’t notice the damage until it’s too late). So even in places I trust, like work, I never leave my helmet around where people could, accidentally or not, kick it or knock it over.
So leaving it outside in a public place is just a nono.
With these two assumptions I would never leave my helmet chained to my bike. Assuming the above some youth might kick it or scratch up the visor or do all manner of bad things just because of the assumption.
I’d leave a helmet in a top box or in the underseat storage of a scooter but nowhere else about the bike.
What you say is very true, but IMHO, all we can do is try to minimise the risk by taking control of the things we can influence i.e.- after we’ve bought the helmet and we are responsible for it. We have no control over what happens to it pre-purchase so no point in worrying about that.