Hello again, O-10. Now to explain more about the doublers. Let's take the first four woodwind books in your Phantom list.
Woodwind 1 is Flute and Piccolo. Yes, this is technically two instruments, so it is a double. However, all piccolo players started on and still play the flute. There is no such thing as someone who only plays the piccolo. That said, a great many flute players want no part of learning the piccolo. In a big symphony orchestra, the third flute player usually is officially the piccolo player (or the second player, in a smaller orchestra).
Same thing with Woodwind 3, Oboe and English Horn. Again, the English Horn is always played by an oboist, there is no such thing as someone who only plays English horn, they all started on and still play oboe. Again, in a big symphony, the third oboist would officially be the English Horn player.
Woodwind 4 is technically 3 instruments, so a triple. Again, though, they are all clarinets, and there is no such thing as someone who only plays the smaller E-flat, or the larger bass. They all started on and still play the regular B-flat (and A) clarinets. However, in a big symphony orchestra, usually the second clarinet player plays the E-flat, and the third clarinet player plays the bass. So this triple is a little more unusual than the first two. There aren't too many clarinetists that would play all three really well, speaking of the top level, anyway.
Woodwind 2, flute and clarinet, is what I would call a true "woodwind doubler", two totally different instruments. This is the only one of the five that is a book that only a true "woodwind doubler" specialist could play.
And speaking of the Frogman, I'm sure he has done doubling work before, being extremely proficient on both clarinet and sax. No sax in Phantom, though. I think he would corroborate the above. A flute player who plays piccolo well can get more gig opportunities. Same with an oboist who plays English horn well, and a clarinet player who decides to learn the E-flat or bass clarinets well. Someone who is a principal player in a large orchestra, however, may never play those other instruments, and may never have, except out of curiosity in a practice room.
And Frogman, if you see anything to correct or hopefully clarify in either of my posts today, by all means chime in!