@Altitude
The physics here are that the string vibration is much more pronounced above the area where a P pickup is than it is at any point closer to the neck. The subjective I’ve read is that pickups have a harder time, all else constant, “reading” the string when it’s moving a lot than when it’s moving a little. And lower strings move more than higher ones in general.
If that is true, it explains why P basses with only the one split pickup tend to sound a bit muddy down low. Adding a bridge pickup helps, because that pickup gets to read the string at a point where the amplitude of the vibration is less. Also BTW, notice that as extended range basses became more popular in the 80s and 90s we saw some new pickup configurations emerge that moved the pickups further back in general. Presumably to address this issue.
But I'm getting the sense from your feedback that choice of P pups and to a lesser extent strings can go some way to addressing the issue.