I guess people would want to run a watch dog to sweep charges to that address without publicly announcing they lost their wallet.
Other use-case: I found a lost wallet. Of course I would want to likewise run a watch dog on that one.
I just imagine some key of some miner leaking and 60,000 users importing it hoping to be the lucky sweeper of the next automatic mining pay out .... hmmm ... most likely the winner could only be some pool that has such a watch dog on their own.
I'm more referring to the use case that some party puts 1 BTC in a private key and distributes it like a coupon code, or as a refund for something, or when you're redeeming a Casascius coin. Or in the case of "buried keys." I personally believe it's a waste of time to put any effort towards keeping those keys around, because that key is dead. No one has any reason to ever send that key any money, ever again. Sweep it and move on with your life.