I'll have to concede that it's possible, but with the drawback of loss of output & back to not sounding as good as a single coil.
Does any manufacturer actually wire their inline humbuckers in parallel? I know DiMarzio allows the option with four conductors, but I think Nordstrand wire theirs in series by default. 33% output loss from series to parallel, that's not unnoticed.
As far as reducing the amount of windings, again with output loss. There's a limitation with the narrow J housing & aperture.
I've heard & played my fair share of parallel humbuckers & not even close to single coil character. However, we're talking about a switchable design, where the pickups weren't actually designed to be run parallel permanently.
Nordstrand could probably get close in their Big Split housing.
You're hung up on lower output level being "loss". It isn't. Professional dynamic microphones have much lower output than higher impedance "amateur" ones. But they also have a lower source impedance, and the benefits of that outweigh the "loss" of level, to the point where all the serious microphones are low impedance designs. Granted, that's not how Leo wired basses, but It's how I do. By reducing the source impedance, you get:
1) Lowered cable loading sensitivity. In fact, to counter the "thin" thing people talk about with parallel pickups, you capacitively load the pickups in the bass before the volume control. Want to run a 40 foot cable? with lower impedance, you can, without your bass sounding dull. Microphones often run hundreds of feet of cable, and they work fine - why? Lowered source impedance.
2) Tone tunability - by changing the capacitance in the on board load, you get the same response change as changing the number of winds on your pickup. Want the sound of a "hotter" or more vintage pickup? Change a capacitor - it'll cost you half a buck, and you'll know which way the resulting sound will go. A pickup swap is a hundred bucks, and it's usually a crapshoot as to which way things are going to go.
3) Volume controls that work as volume controls - with the loading cap on the same side of the volume control, the volume control is not longe in the middle of a filter. Lower the volume, the volume goes down. The tone stays the same.
4) Lowered sensitivity to hum and buzz - one of the reasons for low impedance microphones is they are a LOT less sensitive to external noise fields.
5) Lowered loading by DI's - a lot of DI's dull your sound. With a lower impedance source, that doesn't happen.
So, the drawbacks of a lower impedance instrument? You need a quiet boost pedal first on your pedalboard to overcome the noise of some pedals. That's it.
The "single coils sound better" thing is a myth. There is no real reason that you can't make an inline hum canceller that sound as good as a single coil. With parallel wiring, you can certainly make an inline hum canceller with more bandwidth, a higher resonant peak, and/or a brighter sound than a single coil - the hallmarks of what makes a single coil pickup sound good can be outdone by simple engineering, if you know what to do.The tough thing about doing a REAL test to prove this is that you need to do the test in a completely hum free environment. If you don't, the "single coils sound better" folks will hear some hum and....always pick that sound as "better". I'd bet if you did a good double blind test in a hum free environment, and added a bit of buzz to the hum canceller, the single coil folks would pick it as "better".