Yah. I used the low A often enough, I really didn't ever seriously considering low Bb horns.
RE: Heaven for necks, at least in the bari sax world, the bigger the horn, the more mistreated it is. I'd have no problem believing that the neck was damaged too badly to be repaired and/or it's sitting on the school's repairman's shelf because it needed repair and then was never picked up. Or, as another theory, I occasionally played multiple instruments, even in high school. It's possible that the neck was accidentally put into, say, a bass clarinet case after a gig, then the bari just sat there for years because nobody wanted to play it. Hey, that's what happened in one of my high schools.
Or, of course, there are bari sax neck fairies, just like the tooth fairy. Put a neck under your pillow and the next morning you'll have a shiny dollar coin.