There is no limit on the number of sounds if you want every keyboard to cost as much as a handmade finely tuned professional musical instrument.

No, but the more sounds you use, the more precise everything has to be. Just think of a machine that recognizes blue, red, and yellow as compared to a machine that recognizes all 24-bit colors. Aside from everything else, how on earth would you calibrate the sensor?

You could do something like keep the frequency offset between keys constant for all keyboards, but add some way of shifting the frequency of all of the keys by the same amount. It seems feasible to me, but I have no expertise in the area. The difficulty could prohibit an infinite set of configurations, but it could easily allow for a small set of configurations for cases when a few keyboards are in close proximity.

It would be trivial to use the same synth hardware and warp the oscillator that drives the overall synth by a couple ppm higher or lower.

It would be a lot easier to encode at the message layer.

You are all talking around a FDMA spread spectrum implementation and I'm saying a CDMA would be a lot simpler to implement...

CDMA? Are we still talking about unpowered keyboards that send keypresses with the audible sound of the key striking the board?

CDMA is a neat scheme, but a single mechanical keypress generating a series of bits (at least 8) sounds awfully complex.