You are essentially correct, but it might be good to look at this from a couple of angles. Single coils are single coils, right? Well... sort of. Lets take two single coils with very different sounds...
Compared to other single coil designs, such as the ubiquitous Fender single coil, the bobbin for a P-90 is wider but shorter. The Fender style single coil is wound in a taller bobbin but the wires are closer to the individual poles. This makes the P-90 produce a different type of tone, somewhat warmer with less edge and brightness.
This is essentially the practical application of what you have listed in your question, but it is quite a big, bold difference. Subtle differences in construction make a more subtle difference...
Scatter Wound is the idea that the wire is wound in patterns that are not nice perfect rows. Certain winders do it certain ways and therein lies the better part of the nuance of a pickups’ sound. Therein lies the art. A painting can be copied and still be a beautiful painting, but if it had to be reproduced by hand by another painter, the art of the painting would be found in the nuanced differences of colors, brush strokes, and even mistakes.
Can one pickup builder scatter better than another. Maybe, maybe not. But could one pickup builder be said to scatter more consistently from pick up to pickup? Yes, I'd say so. So I'll pay more for a brand-x because i know that the product is consistent, it will sound exactly like the demo i heard.
Then we get to tolerance. Every component (be it an elctronic/electrical or mechanical part) has a tolerance. Bobbin manufacturer-x produces bobbins to a highly precise tolerance, more so that manufacturer-y. This makes the wire layout slightly more predictable. So again, pickup builders who use the more expensive X bobbin have a more consistent and predictable product, but much charge more. Same goes for wire gauge and magnets and everything else.
So now I've got two manufactures one who makes pick-ups which sounds fine, and one who makes picks which are very tightly spec'd and manufactured to a high tolerance from the ground up.
As a consumer I can buy either, but if I want a very specific sound the higher price tag gets me closer to that sound. Is the sound better, not objectively but it is in line with my expectation more so.
And then... If I can produce things to a tighter spec, I can diversify in a narrow space. Trad Telecaster pickups "all sounds the same" except you can get 52s, 54s, 56s, 62s, 68s and on and on which are subtly different. The R&D time and effort and the quality control required to slice up this narrow market is expensive and that cost is passed on to the consumer. The 52s aren't better, the 68s aren't better, but they are more tightly controlled than the generics.
I'm not really in to expensive pickups, but that's mostly because I've never been after that tone, other than replacing a super-budget humbucker with a $35 P90 because I wanted P90 tone in my second Tele.
If I was replacing the trad pickups on my beloved Tele though, yeah I'd do the research and spend the dollar.