You’re right - I typed more quickly than I was thinking. There are two “this” mentioned and I was thinking of two distinct cases.
With the first “this”, I am referring to the OP about not being able to write to groups as TL0. This is not complained about yet and it’s not a huge issue. If you don’t want to address it, we can close this topic. 
But I do think that allowing TL0 to start messages to staff and to certain groups would be very useful, so we don’t have to send members to email to contact staff for help.
With the second “this”, I am referring to an older situation, long since resolved in our community but still an edge case that I think might be worth looking at. In the past, we provided a link on member profiles in wordpress to send messages to members using the URL method, but removed it because people were bumping up against this cryptic error when they were still TL0 and unable to send PMs. Until we removed the link, we did get questions about it fairly frequently. There is an old topic about this second case: Compose a new pre-filled personal message via URL
Maybe the error could be changed to say “Sorry, you cannot send this personal message because you do not have sufficient privileges” or some such, accommodating both group and user recipients and explaining that it’s about privileges and not some technical glitch.