Why are there 88 keys on a piano? My WAG is that they encompass all the musical notes that the human ear can hear. Am I close?
Nope. The human ear can hear far beyond either end of the keyboard. If the keyboard was to reach the limits of the human ear, it would have so many keys you’d need a skateboard to use it (or the arms of Plastic Man)… 
Not really. Human hearing encompasses a range of about 10 octaves (20 Hz to 20 kHz) at its best, although the high end gets lower with age. An octave is a doubling of frequency, by definition. Since there are 12 keys per octave, that would mean a full-range keyboard would encompass 120 keys. Big, but not impossibly so.
Pianos of all conceivable shapes, sizes and tunings have been constructed through time. In the equal-tempered system, 88 evenly spaced tones gives you enough notes to play most any common musical piece without having to slide back and forth on the bench. (Unless you have really short arms.)
If you want lots of keys, take a look at church organs. Those things are gigantic.
Good information page about acoustic pianos.
So mass production came within 10 years of the expansion to 88 keys. That may have played a part in slowing down changes. More pianos available to more people who use mass produced sheet music that was written for the common piano with 88 keys.
That high note key on the piano doesnt even sound like a note anyway.
To be more specific, the 88 keys of the piano go from A0 (27.5 Hz) to C8 (4186 Hz). two and a half more octaves would extend past the range of good human hearing. It does cover all or most of the orchestral range - I think some very high pitched instruments may extend a little beyond this range, but I’m not sure. Higher pitches would be detectable, but not that musically useful since you lose the ability to detect much of the timbre because you can’t hear the harmonics.
Going much above the C8 using the physical mechanism of the piano might be a little difficult anyway - high piano notes are already pretty weak and “plinky”. Getting any sound out of even shorter / thinner strings mounted on the same sound board might be difficult.
Bösendorfer currently makes pianos with 88, 92, and 97 keys. I’ve heard one once in person (and not in a concert) and the more keys made such a more beautiful sound (although, it could just be the really pricey piano too).
…but the same pitch on a violin certiainly does. (It’s much better on a good piano, mind you.)
Anyway, agreed with DeVena - it’s the result of the convergence of piano development and mass production.