I believe there are times when it is favorable to "burn" ether or another cryptocurrency, i.e. lock up the money in an unowned account. For example, the decentralized market place OpenBazaar discusses proof-of-burn to establish a user's reputation (https://blog.openbazaar.org/proof-of-burn-and-reputation-ple...). Burning coins allows a user to show they are invested in their reputation on the platform, without being forced to pay money to a central party.