Every player has the right to leave a tournament at any time they choose, either by outright quitting, or by shoving all-in until they lose, or by not exercising an available re-buy option. Players also choose when they want to (or are willing to) be eliminated via bet/call/fold decisions.
Nobody questions if those actions are fair; it's purely the prerogative of the player -- of all players, in fact. So none of those related "player's choice" arguments hold much water imo.
And I'm not ducking anything. I simply see no inherent unfairness in awarding a prize to players who eliminate other players from the tournament. It is the entire premise of any tournament to eliminate players -- even in non-bounty events. And in those non-bounty events, a player is also rewarded for eliminating a player -- directly, by taking ownership of their chips, and indirectly, by gaining increased equity (as fewer obstacles remain between the player and the money payouts). In a bounty tournament, it's just another prize awarded to the player who eliminates another player.
Perhaps looking at a re-load tournament structure may provide some insight. In these events, half (or other predetermined portion) of every player's buy-in stack is initially withheld. If a player is felted and loses their initial stack, they 're-load' the balance of the withheld chips and continue play -- and in the case of a bounty tournament, the felted player retains their bounty chip, because they have not yet been eliminated from the tournament. It's essentially a forced re-buy/add-on that is pre-paid and enforced automatically for all players.
And what happens if the player decides to quit rather than to continue with the balance of their pre-bought chips? Good question, and yes, I've seen this scenario actually occur -- either the player decided it wasn't worth the effort with a miniscule stack (in the case where a much smaller percentage of the original buy-in chips were withheld) or the player wasn't feeling well (essentially causing them to perform poorly) and decided to withdraw rather than suffer further (both physically and mentally). I would argue that the reasons for quitting are irrelevant.
In both cases, the bounty chip was awarded to the player deemed responsible for their exit by winning their initial stack (this was not my event, btw). One could certainly present a strong arguement that since the player(s) voluntarily quit while still having chips that were bought and paid for, the remaining re-load chips should be put into play and subsequently be blinded-out, with the player's bounty chip awarded to the player who eliminates the remaining chip stack (which is how I would handle it, were it my event). Alternatively (and easier for the director and remaining players), the re-load chips could never be put into play at all, with the value of the bounty added to the prize pool (although this should be a formal rule already in place, and not a real-time TD decision).
Compare that to a re-buy single-bounty tournament (vs pre-buy/re-load), where the player has the option to extend their tournament life (but is under no obligation to do so). By choosing to not re-buy (reasons being irrelevant, as it is his right to do so), the player is eliminated from the event as a direct result of the player who won their last remaining chips. Thus that player is responsible for the player elimination, and should be awarded the player's bounty chip.
I still fail to see how this could be considered to be "unfair". Unfair to whom? If every bounty chip in play is awarded to a player who eliminates another player, everybody stands on common ground. Eliminate a player, collect their bounty chip. Simple.