I have a humbucker with a tapped screw coil, so bear in mind my opinion will be slightly different. That being said I will opine as well on a pickup I had before which was wired the same way except without the option to run the screw coil at 2 different outputs.
The tapped humbucker is 7.1k in series, and 6k split... In parallel I can roll in any or all of the tap. The reason you would split vs. series/parallel a humbucker is purely related to sound IMO... No matter how large the difference between the coils there is always some frequency loss when you introduce another coil to the equation. This doesn't make it sound better or worse, just different. I can't get that sweet-yet-clangy SRV neck pickup sound in series or parallel, but split it's right there. I can't get that smooth, sing-y santana tone, or that fat and clear sound jimmy page got with it split or parallel.
Parallel I think is better for a volume-drop clean sound when you're playing on the edge of breakup for some added dynamic color. Split IMO is better for when you absolutely need that extra treble content, one example being that twangy country bass (but then again gretsch does it really well with humbuckers so what do I know)
Honestly, in my guitar I think it's overkill... The differences I'm beginning to realize are so minute that it's not really worth all the trouble of wiring the guitar, plus ordering a custom pickup that has a tapped screw or slug coil.
Although, if I were to do it all over again, I would probably still get a tapped humbucker, just with the slug coil tapped. IMO slug coil > screw coil when it comes to tapping humbuckers.