I can give you a plus one on that as my favorite "technical" feature.
My absolute favorite thing though is a bit more abstract. You know how you pick up certain guitars and they influence your playing? Certain songs come to mind, and whatever you play you play it a little differently with that guitar. You put some in, and get some back. Like a conversation. I have a similar thing with a well placed BKP. The way they sound is not just something that comes out of the speakers, it feeds back into the playing.
I guess part of that is what you say too, how they are players pickups, giving you the chance to fully hear what you are playing, not masking it, making you more aware. But even in the same guitar a Stockholm makes me play very differently than a RY.
BKPs seem to not just be some part in the chain, but part of the instrument.