The very early Suzuki books were an attempt to expand the success of the Suzuki method to double bassists. It didn't go over well for bassists, and the method is still more or less ignored, today, even after the series tried to learn from its mistakes. Check out the early Suzuki books from the early 1990s, and you'll see what I mean. The problem was the editor at the time had to adapt the repertoire for double bass. Unlike the other string instruments, you can't play any of the Suzuki rep in one position on the bass. So while the young students of the other instruments in the string family don't have to worry about shifting so then can focus on bow hold, tonalization, posture, etc, and most importantly having fun because that is the power of the Suzuki method, young bassists had to screw around with a really weird "pivoting" + shifting system almost right away halfway through Book 1, in order to play the repertoire. I use the word pivoting loosely because it wasn't really taught properly as pivoting. It was notated as some kind of "low 1" "high 1" pain-inducing monstrosity.
The reason the Vance method works is because it fulfills the aims of the Suzuki method in terms of pacing, scaffolding, getting a satisfying sound, introducing mechanics, and most importantly, nurturing an innate love for music, but unlike the Suzuki method, repertoire was selected and arranged around the bass as opposed to the Suzuki way of forcing the bass work around the repertoire.
I'm sure there are still bassists who use Suzuki method, and I'm sure they will chime in, hopefully. But the sense that I get is that when you hang a shingle as a "Suzuki" bass teacher, you'll get more customers because parents don't know jack s**t about pedagogy beyond recognizing the "Suzuki" brand and the assurances that come with hiring a Suzuki-certified teacher. If you hang a shingle as a "Vance" method teacher, nobody, outside of bassists who don't need to take early childhood bass lessons anyway, will know what the heck Vance method is (or Simandl, or Rabbath for that matter).