Nobody can hear fundamental musical pitches up to anywhere near 20,000 Hz, not even new-born babies with perfect ears. The upper range of human hearing is only useful for hearing overtones and harmonics that are basically "felt" rather than "heard".
There are a few notes above the range of the piano that can be heard, but they are not musically useful. A very skilled violinist can produce these using harmonics. You could produce these pitches with some analog electronic synthesizers, but not with an acoustic instrument. If you try this yourself, it will occur to you that you've never heard these pitches used in any actual music because they are not musically useful and because few people can hear them, and those that can find them unpleasant to listen to.
Neil, piano design aside, there's a fundamental misunderstanding in your line of questioning. You read in a book somewhere that the range of human hearing goes up to 20,000 Hz. Well, so what? That is only a theoretical construct. Different individuals have different ranges of hearing. Most people can hear the pitches in the middle of the theoretical range of human hearing more or less the same, but there is a tremendous variation among people in how they hear pitches at the extreme low or high end. For virtually all people, the range of hearing decreases with age. Men as a group lose high-end hearing sooner in age than women. I am a man who has always been regarded as having excellent hearing, but at the age of 34 I discovered in a recording studio that I could no longer perceive a loud sine wave at 11,000 Hz, while younger women in the studio could hear that pitch (and clapped their hands over their ears in pain).
Furthermore, the frequency response of the human ear is not at all linear. It doesn't even follow a mathematically describable curve, because, again, human hearing is not based on mathematical laws; it's based on the physiology of the human ear and the brain. The loudness with which people perceive extremely high pitches is sharply attenuated.
A statement like "the human hearing range goes up to 20,000 Hz" is like saying "the range of human height goes up to 7-foot 2-inches (218cm)." Does the clothing industry only mass-produce clothes that fit people who are 7-foot 2? No, they make clothes that average people can wear. That way they sell more clothes.