At the moment, you can configure users to be allowed to send direct messages either to other members of the team or to anyone on the server.

I'd like to make it so that normal users cannot start direct messages at all.

My particular usecase may be a little out of the sweet spot - I have created a mattermost for my children (quite young) who I want to be able to chat with while they are doing their home learning, but don't want them using public chat systems. I am happy for them to interact with each other in the public channels I have created, but I don't want them distracting each other with lots of messages that are difficult for me to see.

My favourite scenario would be just for non admin users simply not be able to create new direct messages.

While this is specifically for a home learning situation, I believe it could be useful in a corporate world too, although there it would have to be per user - it might be the kind of restriction you'd want on external users from outside of your organisation.