String height is a personal choice for each player. You are quite right that the tone can change. I believe that there is a wide range of string heights that have a good tone. My action is high enough that I can bow easily, amplify with a microphone, and get some good one finger right hand pull. It is also low enough that I can easily finger the left hand with the velocity that I desire. Many years ago, I played gut strings for a while with high action. I have chosen to use steel and a reasonable string height that I am happy with my tone and facility. At some point with really low action, the tone becomes more "sitar-like". At this point the volume is significantly reduced. At the other end of the spectrum, there is a point where the action gets so high that it can choke the bass. With higher action, there is a point that the bass will not get any louder, just harder to play. A good luthier is essential to getting your bass set up so that it works at the height you choose. Obviously if one chooses really low action, the fingerboard must be perfectly planed so there are no buzzes or high spots that choke the string. Every bass is different and the strings you choose also add variables.
