I think it's more about how and what you play. When I played bari in a saxophone octet and we played songs like "My Funny Valentine" I had to play in a differnt way. Often long legato tones. When I play Rockbari it's more about to play in a percussion-like way. The setup was differnt as well. I played a Brilhart HR in the octet and I use(d) a Dukoff D9 in Rock. Both idioms need air but you must use the airstream in a differnt way.
I also think we can forget the talk about that a bari needs a big person to fill the tube with air. There was a small guy in Joe Liggins Band ("The Honey Dripper" -45, some people says that it was one of first Rocksongs ....) called "Little" Willie Jackson. He played great bari. On the pictures I have his low Bb bari reaches to his knees.
Thomas