efbgen, I wanted to add my voice to the chorus of sympathy. I have a number of heirloom pieces (not scarves) that are important to me both emotionally and in terms of expressing my style.
My vote is to wear the scarves. It seems that either you could keep them packed away and they will still deteriorate, or you could wear them and they will deteriorate. I suspect that you will get more joy out of the latter. Once scarves are folded/tied about your neck or the handle of your bag, that hides a lot of imperfections.
I like the idea of making jewelry out of a bit of the scarf when it gets truly unwearable.
ETA: Or, if the scarves are similar or at least matchy-clashy you could take the good bits from each one and piece them together into a new scarf??
This is not quite the same, but I had a tablecloth that had been given to my grandparents as a wedding present. It was pretty worn and not really usable as a tablecloth. I cut it up and made dishtowels out of it. With use the dishtowels eventually became absolutely shredded and I sent them off for textile recycling. I'm very glad I took this route, I think it was the right thing to do.