You can't communicate with quantum teleportation. It sends random "information" (not information at all), because you can't control how the quantum waveform collapses. So you have to collapse the waveform, create a key that encodes your collapsed form to the information you want to transmit, and then transmit that key slower than light i.e. with radio.
I guess you could argue that since the keys themselves are also indistinguishable from noise, we wouldn't detect slower-than-light key transmission either, though.
> it is not possible for one observer, by making a measurement of a subsystem of the total state, to communicate information to another observer. The theorem is important because, in quantum mechanics, quantum entanglement is an effect by which certain widely separated events can be correlated in ways that suggest the possibility of instantaneous communication. The no-communication theorem gives conditions under which such transfer of information between two observers is impossible.
I agree with you, this is impressive and probably will be very helpful some day.