That forces one to spend extra time to restart things that were already started. At the same time, I can see the need to allow people to delete things they might have realized they revealed too much in (or some similar reason).

My suggestion would be involving mods (although I hate to put more work on them) via a process that allows OP to request deletion, then hide it until a mod can decide if it should be deleted entirely, or just the username disassociated from it so the conversation isn’t abruptly yanked from participants.