As much as I admire Turing (I've often wondered what our world would be like if he hadn't died as young as he did), I've never been that convinced of the value of the Turing Test.
Given a choice between
1) software that can carry on a convincing conversation about sports, politics, music, movies, current events, etc. and
2) software that is obviously an AI that can do medical diagnosis and treatment planning better than 90% of human doctors,
and I'll take number 2 in a heartbeat.
In the future an AI that can do both will probably be developed, but right now I genuinely believe more effort should be spent on solving problem #2.
My guess is that Turing thought that you wouldn't need to make such a choice, and that a robot that could analyze the intricacies of medical diagnosis could surely be able to talk about the weather. It's much like you don't have to make a choice between your program being able to do medical diagnosis and the program having a full-color graphical interface (or even a touch interface on your phone, these days).
In other words, I think that Turing was simply wrong on this point. Though, it's not hard to imagine a future where it becomes cheap to make a program pass a Turing test, changing our expectation of what the user interface for a computer should be like.
When building chatbots, you face this choice. You can either try to poorly impersonate a human, or you can cop out that you're a chatbot and tell people what you are capable of assisting them with. One leads to frustration for the user, the other to potentially useful outcomes.
Given a choice between
1) software that can carry on a convincing conversation about sports, politics, music, movies, current events, etc. and
2) software that is obviously an AI that can do medical diagnosis and treatment planning better than 90% of human doctors,
and I'll take number 2 in a heartbeat.
In the future an AI that can do both will probably be developed, but right now I genuinely believe more effort should be spent on solving problem #2.