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.
deleting entire chat for both sides surely gives us control over our privacy and this feature should remain as it is. however another feature could be introduced for both participants to come into an agreement preventing deletion of the chat, a certain time (1 minute) limit could be allowed to delete or edit the messages. in groups admins can change whether the chats can be deleted or not but of course members will get notifications to agree or disagree.