Ideally, a boss should be the highlight of a particular level or section of the game you happen to be playing through and there are various things that determine whether a boss fight is great or not. The first one is that they are fair -- nobody likes a boss with haywire attack patterns and moves that cripple you instantly. The second is a clear strategy that is obvious to the player relatively early on in the fight. It’s no good being at death's door when you finally figure out what you should have been doing. The most important thing a boss encounter should be is consistent. Once you have figured out a strategy it should work every time. There are few things more irritating than thinking you have a boss fight figured out only to get destroyed on another run.
This brings me to my main point regarding boss health bars and why they’re so important. Take a look at the RAAM fight in the original Gears of War (sorry Epic); there was nothing to indicate that you were actually dealing damage to him. Usually a boss will have some kind of audio or visual cue if a health bar is absent, whereas RAAM had neither. This results in significant frustration as the player can easily be confused and if they don’t feel like what they’re doing is right, they can try something completely wrong. Including a health bar for a boss gives the player the information they need, like whether or not what they’re doing is causing damage and how effective their attacks are.
Stop looking at her butt and focus on the health bar, that's the important part.
Including a boss health bar could break immersion for some players; however, I would argue that if your boss is done right, the health bar shouldn’t distract you anywhere near that much. There is always the part of your brain that is aware you’re playing a game, the part that determines whether or not what you’re doing is the right thing at the time based on your experiences of playing other games. Also, boss encounters that do not have health bars tend to have very obvious visual cues for dealing damage -- Dead Space and God of War are great examples of this.
The aspect of immersion has become a big part in gaming and developers are always trying to make you forget that you’re playing a game. There’s no doubt that including a health bar could be viewed as old-school, but I would just call it good game design. If a boss encounter is done how they should be done, the inclusion of a health bar doesn’t matter, it’s something that your brain just picks up on and takes note of. However, it’s when boss fights are done horribly wrong that the absence of a health bar becomes a big deal. Not including a mechanic that conveys vital information to the player is simply inexcusable, especially in a time where games are trying to reach more people than ever before.