Wow. That seems, um, like a design flaw.
Do other brands/types of basses do this?
The pickups on a Fender Jazz are reverse wound, reverse polarity from each other. When they are both on ten there is phase cancellation that is most noticeable. Turning one down just a bit diminishes the phase cancellation noticeably. The pickups also are hum cancelling.
It has a different quality than a Precision. So it's a design choice for all of these reasons and not a flaw. A Jazz is brighter, in mids and highs and less emphasis on the lows. With the pickups spaced wider apart, and the 2 volumes the Jazz arguably has more options. Fans of the Precision, though love it's unique sound.
Many players have one of each to cover a wider variety of styles.
Thank you for this excellent explanation. It makes sense.
(I just have never played a Fender bass so it is all new to me.)
Actually, all it is is the fact that the pickups are wired in parallel, all basses with pickups in parallel will give a slight mid scoop when both pickups are on, and a slight drop in volume due to impedance loading. But the low end does not drop out. It is not phase cancelation so much, otherwise the lows drop out considerably. What is being described here is just the mid scoop, which goes away when one pickup is backed off to about 80%. Everything is still in phase on a normally wired jazz bass.
A series switch like an S1, will raise the impedance and also trade the mid scoop for a mid bump. This is why p bass cuts through, series coils give that mid attack, but with slightly less high and low content than a parallel circuit provides.