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The thing is, often playing the written low A up an octave breaks a line in an unmusical way. It's often better to find another note down low that works with the melody and harmony.
The truth is, most of the time baritone in the big band is really playing a bass-instrument part, similar to the bass trombone's role (and of course, often the bari sax doubles the bass trombone part). However, the baritone doesn't have enough range to complete lines that the bass bone might play.
The solution is to use for the bass parts in the sax section, a true bass instrument, the bass saxophone. I have done this; it works GREAT for low register lines; most bari parts aren't written high enough to be an issue, and when the part runs off the top of the instrument it's almost always doubling one of the higher saxes so it can be recast a bit without sounding bad. It takes some practice to get used to the transposition. When I did this for some months in a big band, I didn't get comfortable enough with the transposition to play faster passages at sight, so I half-assed it and brought the bari as well, and that was too much to schlep. So I gave it up on the grounds of exhaustion; but I'd love to try it again.
