some P pickups are humbucking both halves - why?

[AndyPanda]

So I fully understand how the stock P pickup acts as a humbucker - and I really like the way it has the benefits of bucking the hum while still only having one coil under any given string. So my question is why do some pickup mfgs make both halves of the P pickup a dual coil humbucker? Is that just because some people prefer the sound of both of the humbucking coils under each string (I don't - but I understand that everyone has their own tastes).

I have a P with a Joe Barden rail pickup - and I like it a lot - just one coil per each half of the pickup:

But I see people with the Dimarzio - each half is its own humbucker:

And now I see Norstrand has a P with what looks like two coils in each half (I could be very wrong about that - I should have looked up the specs first, but I'm just going by the picture) It looks like each string gets it's own coil so it should still have the sound I prefer:

 

[line6man]

Is that just because some people prefer the sound of both of the humbucking coils under each string

That's exactly it. Quad coil pickups give some extra variety that appeals to certain tastes.

 

[BassGyver]

The Nordstrand has the same construction as your Barden, except for the small "gap" in the rail, to give a better rigidity to the plastic cover.

I have seen a quad coil (1 coil per string) a long time ago, with a single polepiece per string (like the MM pickup polepieces) but I can't remember the name of the maker.

Edit: something looking like that:
Masters of Wood (MOW) "Snake Eyes" Quad Coil 4 String P Bass Pickup Neodymium • $95.00