It is true that GPS elevation measurements are traditionally much less accurate than horizontal measurements, for a number of reasons.
My understanding is this is because GPS elevation measurements are based on a perfect ellipsoid. These measurements are known as "height above ellipsoid" or HAE. However, we want to know what the elevation is relative to "mean sea level", or the "geoid surface". A geoid model allows translation between the HAE and MSL measurements. These models continually improve, and the NGS puts out new ones every so often. As these models become more accurate over time, GPS elevation measurements become more reliable.
A 20m cliff is quite significant to climbers, but to account for this at a global scale requires a very accurate understanding of the earth's shape. It is much easier to be fairly accurate in the horizontal.
It should be noted that with the right techniques, GPS elevation measurements can be used for projects that require the most accurate of measurements. It just needs to be applied correctly.