The map banter (and other things) are just that - banter. They’re there for flavor. Entertaining flavor, and varied enough that you need to play things several times to hear it all but it’s still just flavor. The comments on career skill use and different enemies, on the other hand, are there for information, to let you know what others are doing and what is happening around you, as you don’t see everywhere. For that reason, I prefer that the banter gets lost to informational comments rather than the other way around. It’s already annoying enough when an Ironbreaker (whose Career Skill absolutely needs callouts) quietly taunts enemies, so I don’t notice I have free hands for killing them for a while. While on WS or Pyro it’s less important, it’s still nice to know that I can give a glance to the kill feed to see which specials or elites don’t need attention anymore.
Okay, I admit, the particular spot you used as example is slightly different, as at that point, the small fry are running away, and unless you do something stupid, you’re safe already. So no callouts are really needed anymore. Beyond a few map finales though, callouts are far more important.
Besides, I have felt that there isn’t a specific priority to them other than whatever starts later gets said. A partial fix would be that if the talkers were different, the lines wouldn’t interrupt each other, only suspend or momentarily silence the banter ones. I don’t know how hard that would be to implement, or how much extra processing power it would add, but one can only mention it and hope right now.