I have to disagree. One of Bliz's best features is their ability to create unique encounters which have their own voice. No one will confuse patchwerk and the four horsemen, for example. If any boss within an instance could have "x" ability, I feel the encounters would lose a bit of their charm.

Additionally, Bliz has implemented a similar concept in past boss fights, (Khaz or Violet Hold). Usually, that random element doesn't add much more than simply another layer of instructions for players to learn.

Yeah, I'm not saying that by implementing a bit of randomness to a boss it would end up with every boss having a chance of actually being some other boss. What I am a bit tired of is simply reading the proper tactics for a boss, and then executing them without much going wrong, if done correctly.
I think it would be an interesting idea to give bosses a sligthly more intelligent AI, for example, so they don't just stand there and take a beating. But hey, I guess that's why I like PVP!

Give each boss it's own signature move or two that defines the encounter (involving specific elements of that boss's chamber, his own established lore, or even just his appearance), but also some random elements from a shared list that change out from raid to raid.

The end effect would be a lot more like high-end PVP arena matches, where you generally know what a particular opponant is likely going to do, but you have to watch out and react to unexpected elements on the fly.

Of course, players could get frustratingly stuck on bosses who get an unfortunate combination of abilities, and balancing difficulty would be extremely difficult, but it'd certainly change up the formula quite a bit.

Of course, if that sort of thing were in the cards, changing where trash stands and patrols would also make getting there a lot less formulaic.