Any attempt to make an "exact science" out of pickup placement, would be predicated on playing songs that only use open strings.
If you play genres of music that require fretted notes, then it is no longer an exact science, because as soon as you fret the string, you've changed the location of all the harmonic nodes. Hypothetically speaking, if there were such a thing as the "sweet spot" where the pickup is in the perfect location (there isn't, but humor me as a thought experiment) then you would need to reposition the pickup constantly throughout your band's set, depending on the key of the song and what fret number you're playing at.
There have been bass designs with movable pickups (the Westone Rail comes to mind) but they never really caught on, because (guess what!) that "sweet spot" I mentioned earlier is kind of a myth. You can play a jazz bass with the bridge pickup, and it will sound good every fret, from the open string up to fret 20. Then you can switch to the neck pickup, and it will also sound good every fret 0-20, even though the pickup is in a different spot. I'm not arguing that jazz back neck and bridge pickups sound identical (that would be a silly argument) but they certainly both sound good. There exists no note on a jazz bass where you have to use one pickup and not the other.
Finally, it's probably worth mentioning piezo bridge pickups. I was briefly obsessed with these in the 90s. The argument goes that, a pickup in the bridge is not affected by harmonic nodes, and therefore ought to give you a fuller tonal response over the whole range of the instrument.