En route to the development of modern microphones, a lot of different technologies were explored. There were piezoelectric microphones. And there are contact microphones, that pick up vibrations by being in contact with something. So, a piezoelectric contact microphone is a real thing. The Ehrlund is also a piezoelectric contact mic. I’ve got one of those, and experienced similar issues, such as feedback and picking up the drummer. But it works fantastic on my cello. Don’t ask me why I have a pickup on my cello.
On the other hand, there are players who love them. One thing’s for sure, no two instruments amplify the same, and no two players have the same amplification needs. I know of no other method than trial and error for finding the right bass pickup. I think the fundamental problem is that there’s no single “place” on an acoustic instrument where the localized vibrations represent the entire tone of the instrument.