For the buyers, I always assume it has to do with taxes. "Proving" you owned Bitcoins a long time ago, and your current riches really came from capital gains and not crime. Or just bragging rights, but it seems like cheating if you bought the empty address.
That part about taxes is not very logical to me, unless the tax office is very inexperienced and naive to believe such a story. If I sign a message from a BTC address that is, say, from 2012 and show it as proof to my tax office, if someone there is intelligent, they will look for a history of transactions that will connect the sold BTC with that address - or they will ask me to transfer part of the funds to that address. That would not be very smart, because those who sell such old private keys surely try to sell the same key more than once, which can put the owners in very unpleasant situations.