Well, Tyzias certainly doesn't look like a bounty hunter and Tagora's confirmed to be weak so he'd be lousy at it. I was picturing Tegiri hunting actively while Tyzias and Tagora stuck to paperwork, if that makes sense.
You seem to have a lot of faith that Alternian Society would care about whether or not aspiring Legislacerators can actually handle a fight. There could be less bounty-huntery types, but what they are capable of or want is not exactly a factor when talking about the structure of Troll Society at large.