I think the main reason there aren't many of these is because there are only a few positions that are different sounding enough, while still sounding "good." I took on this idea with a pickup testing bass I had, built a sliding platform to mount pickups to and test how they sounded in different spots.
Here it is, posted in another thread
When testing, I found the best sound from many pickups were within the musicman 'sweet spot', where the pickup is in stingrays and sterlings. The frequency response was great, it seemed to have enough treble that the tone knob made a good difference, but still had plenty of bass oomph that it wasnt thin or lacking in warmth. BUT it wasn't really a large difference that it could not be achieved through amp EQing or a preamp.
There were definitely a few spots where the pickup sounded a bit bland, kind of like hitting a dead spot on a neck, so there are definitely reasons behind specific placement of pickups. If I had a single pickup bass, I would always put the pickup in this spot (MM sweet spot), but I think multi-pickup basses have an advantage, because basically you can take the different sounds of each pickup location and blend them together into one sound, unattainable by a single pickup.
Honestly the ideal would be to have a few pickups with their own volumes (or at least individual on/off switching) and a master volume pot, so you could blend each into your sound. I think that would be a great natural (passive instead of active) sounding way to get some really good usable tones. As always YMMV, these are just my observations after testing a bass with a movable pickup, and while it does allow a range of tones, it is not the most efficient way. I did have a hard time getting a good balance of it staying put while playing, and ease of moving it when I wanted it to.
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