Bear in mind that I don't own a "classic".
I think I would ride mine, but I have no interest in museum pieces. For me the kick comes from riding, not owning.
I have noticed that both backpackers and cyclists tend travel in a "gear bubble" and imho pay too much attention to having the "right" bike or the "right" gear.
I would much rather have an *.mart knockoff MTB that I could ride instead of a "classic" that I could only look at.
All that being said, I have hopes of rehabilitating an old balloon tired cruiser and using it for a winter commuter this year. It will be a rehabilitation as opposed to a restoration because I plan to ride the thing. If I can't find an old one at a flea market or thrift shop, then I will buy a modern copy, but I would prefer the older one because the idea of reusing old "junk" appeals to me in an eccentric way.
Dan