Removing the Conversation Tab is being reviewed by the feature team.
For deleting chat messages, please following progress here: https://microsoftteams.uservoice.com/forums/555103/suggestions/33535006.
An error occurred while saving the commentAnonymous commented
For sure we need to be able to delete conversations. What other app doesn't allow you to delete content? I only use Teams because certain co workers insist on it - partly because I don't have total control.