pickup's voltmeter readings

Vintage pickups used to be all the same

with the same output on all pickups, you would get a volume drop
switching from the neck to mid to bridge

most "botique" strats sets have readings where the bridge is the highest output
then the mid, then the neck...they are "calibrated"

higher output neck pickups get muddy, you have more string definition
at the bridge, so you can increase it a bit more without getting muddy

from a physics point of view, there is a larger amplitude of string
movement at the neck, thats why it's louder,

well, the ohm reading isn't the only factor, as magnet type and strength is a plays a part

different magnets have different "tones", and strength, Ceramic sound diff than AlNiCo

and while the 10k neck may be more balanced with the 12, it would probably
be a bit dark, and muddier

the "balance" comes into play when switching between neck and bridge
you may have to adjust volume, or running neck and bridge together,
the bridge would overpower the neck

the only "matched" set I have is the Seymour Duncan Seth Lover
and BB1/BB2 in another...the are .5k apart
like neck 7.25 - bridge 7.75 k
or somehting like that

great all around, but if you want a killer mega bridge, may have to live without "balance"
not biggie...many of the big boys only use the bridge

The physics part part is extremely complicated, and the others factor beyond those described by Rick are the fact that reading a DC (fixed) Ohm measurement is NOT real life.  This is because your pickups are AC (changing), as are the notes played!  Therefore the impedance and phase angle come into play.  Higher frequencies in inductive circuits will have a higher reactance, which is the AC version of your ohm reading, and a higher output. On top of all that, playing high on the fretboard (all strings) shortens the length of the string as far as the pickup is concerned....that's why high 20's frets played nearest the neck pickup sound like one might think they would be plucked at the bridge...the pickups respond to STRING MOVEMENT (shorter movement at the ends of the string lengths than the middle areas).  Active pickups & EQ make sense regarding many "movement" thoughts about pickups.
Rock On & Keep the Faith,
Rocket

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Stu you are right on the money here.   It's all tone and it's not all electronic.  I've seen guitars of the same brand, model and equip. and they sound different.  Stats of electronics is a good starting point but trust your ears.   Everyone's different and lets not even begin to do this with amps.  It will go on & on & on & on.......   Ha!