Electromechanical subtractive crossover?

[Mr Evil]

I just came across the idea of subtractive crossovers, and on reading about them the first thing that popped into my head was that they could potentially be used as a form of error correction. Imagine the following:

A 3-way active speaker system. First the input signal is low-pass filtered and fed into the woofer. The woofer's output is measured using whatever sensor is convenient. This is then subtracted from the input signal, delayed, low-pass filtered at a higher frequency and fed into the mid-range driver. Repeat the same up to the tweeter.

Ideally, all distortion from the woofer is cancelled by the midrange, and all midrange distortion is cancelled by the tweeter, leaving the only distortion products up very high, hopefully above human hearing range. Of course it's not going to be perfect in reality, and I would imagine it would require more precise measurements to align everything than most people here would have access to, but still perhaps the idea would be useful to someone.