Back in the days of the humble video game arcade, boss battles were designed to be as unfair as possible. The idea was to hopefully push the player to insert another coin to continue after they (inevitably) died. Boss battles tended to mark the end of a stage or level, giving the player a very clear sense of progression in what was usually a hectic, but formulaic environment. It is this particular characteristic that was carried across into the advent of the console, as the need for a player to pay more to continue was obviously unnecessary.
The concept of a boss battle has barely evolved in the years since its arcade prominence.
Having said that, the concept of a boss battle has barely evolved in the years since its arcade prominence. Games are still using the same formula for a boss battle that they always have: use them to mark the end of the level, and ramp up the difficulty for no real reason. As much as I love the oft-forgotten FPS, XIII, it has the irritating tendency to unceremoniously throw a boss encounter at the player. These boss battles can only be played out in one way: pump bullets into them. This is at odds with the basic freedom allowed for the majority of the game, as there is a choice to play it stealthily or more gung ho. The presence of normal human bosses that can soak up a huge quantity of bullets somewhat illogical as well, given the world of XIII is not supernatural or otherwise fantastical.
There are certainly ways to innovate the boss battle, and Nintendo have done a fairly good job of it over the years. Both the Zelda and Metroid series' feature bosses that are designed to specifically utilise the training that the player has just received. For example, in most Zelda games, various tools and weapons are introduced to the player in stages, staggered to ensure that they are able to get the max enjoyment out of using them before something new comes along. Each boss in Ocarina of Time, for instance, is designed to test the player's ability with a new tool before the next one (and will usually employ the previous skills learnt as well).
What would happen within the story if the adversary were allowed to survive for another day?
So, what could be done with the XIII example? While the game is fairly story heavy (and the boss characters must absolutely be defeated in order for the story to proceed), allowing the player to approach it in the same way that they approach the rest of the game would be a great start. It would certainly suit the world of the game to attempt to assassinate the target in a quieter manner, rather than the bombastic gun battle that occurs. Granted, this might remove the challenge of the boss fight, but it would keep the integrity of the world and the rest of the gameplay experience consistent. In fact, one could argue that XIII really didn't require traditional boss fights at all.
Let's look at a hypothetical game instead. Would it not be an interesting idea to not only give the player choices within a boss battle itself, but actually allow the player to decide whether or not it occurs at all? Let's say, for instance, the story has delivered a protagonist to a potential stand off with an adversary. If the player decides not to go through with it, how would that affect the world? What would happen within the story if the adversary were allowed to survive for another day?
The traditional boss battle is not something that needs to be removed from this point forward. It would actually hinder certain games; Super Mario Brothers and the Metal Slug series owe some of their charm to their respective boss encounters. The problem with boss battles is that they're too rooted to the concept of being a standalone entity. As a result, they will continue to feel foreign to a growing number of games.