The feature team has decided to decline this request after careful consideration. Thank you for the suggestion and all the feedback.
It looks like some people in the thread below have figured it out — we actually have this. You can start a chat both ways; the system will automatically recognize if this person is on Skype for Business or on Teams.
Thanks and let me know if you have any questions.
SuphatraDavid Johnson commented
We had users who tried Teams, decided they didn't like it and went back to Skype For Business. In this case trying to message them from Teams sends the message to their Teams account (no Skype logo), which they aren't using. They see nothing in Skype, and only receive a missed message email several hours later.
If the Skype user messages someone in Teams from Skype For Business the message shows in Teams with a Skype logo against it. Teams users can reply to these messages and carry on the conversation, but after a while the Skype message will disappear from Teams and the Teams user is unable to message the Skype user again.
So I think our problem is that users who have tried Teams once effectively break messaging between the two products because there's no way to specify a Skype account when starting a new conversation.
Performance has been and continues to be a big focus area for Teams. One main area we have made improvements in is responsiveness for the most frequent user actions of switching between Chat, Channel, and Activity. We are also focused on reducing resource consumption and application load time. More improvements are on the way.