Robotic tuners actually do exist for guitars – but pianos have two to three strings resonating in unison per note, so tuning is not quite as simple. Nevertheless, it seems that a tuner could easily detect beats (probably using some sort of FFT/spectral analysis) and turn the tuning pegs automatically.
I’ve thought of this also. But it might have to be a self-tuning piano, rather than a piano tuning machine, though.