They don't as far as I know, because they are valued for their functional use cases, although a special chunk of copper or gold might fetch something extra from somebody due to historical significance, or whatever. What I guess is confusing me is this "proof of work" idea. There's no value in that. It's just there to ensure rarity. But we could ensure rarity with a ledger that was populated completely from the beginning and didn't allow for anything more to be added. There'd be no way to make more. You may say, why should anyone offer money for those rare bitcoins? I don't know, same as I don't know why wasting energy mining them would give them any value. They're rare, and like gold, diamonds or whatever, if it's rare and you've got the real deal, I don't care how hard you had to work for it or not. If it's the real deal and it's hard to come by, why does it matter how hard it was to produce? So why the mining? I get the impression the mining is the mind trick for this scam. Maybe all money is a scam, but I don't think so when there's real power in control of vital resources that's issuing it.
Update: I understand now that the mining is tied to transaction processing as well. Somebody has to pay for that, of course! Still, there are transaction fees on top of that.