Let's think of a scenario where this could work.
We make it to Andromeda. We engage in civil conversation with the galactic 'council' of Andromeda, so as to limit or avoid any fighting between us and them. Due to some demands from us that many people dislike, some of those people depart from our Arks and seek out to do things their own way; even if that means killing Andromedans. Seeing as we are venturing out in exploration missions, we are told about this and are tasked with dealing with them. Then it's just a case of making each bounty hunt different and interesting.
Could something like that work? Maybe. It depends on the overall plot of the game. Bounty hunts themselves could work, but there must be a reason for them, and they must make sense within the game and lore.
For example. Andromedans would unlikely give us bounty missions, because they don't know us. They don't know how we deal with criminals. How we go about executing a mission. Our means are a complete unknown, so they probably would not gives us contracts on their own people, even if "by any means necessary" was on the table.
I would however like bounty hunt missions. Particularly ones that are lengthy and meaty. I want to feel like a hunter when I chase them.