Being able to delete your own messages can be handy at times, but ancient history is most useful as something to refer back to, and should be preserved. I feel it would make more sense for message deleting to be limited to a certain amount of time after the message is posted. It could be a few minutes, it could be a few days, but a limit feels important. If you keep a conversation around because it has a lot of good information, then someone decides years later that it isn't worth anything to them and they delete their messages, they've ruined part of the experience for you.
Proposal:
Allow the message deletion limit to be decided by the group admin, or by the individuals in a conversation. The limit could be hours, days, or never. Changing the limit could notify everyone in the group, or require agreement in one-on-one conversations.
Controlling your chat history should apply to both parties, not just the one who wants to delete it.