I think ANet said it best (paraphrasing) "You know how trinity based fights are only fun when something goes wrong? That's the basis of our entire combat system."
An example of this for me was when Cata just came out, I was tanking on my Pally with friends and we were in Stonecore doing Ozruk(heroic) and for whatever reason people died one by one, I think I solo'd the last 5% or so on my own and it was exhilarating because I had to do it myself and there was no one there to rely on. I had to manage my skills and use them at the right times in order to not die. It's everything GW2's combat system is, but ALL THE TIME.
How strange, I had a similar experience, except I was on my mage and I soloed him for the last ~5%, with the rest of my party cheering me on in vent. It came down to the fact that I've played my mage for so long and know every trick that allowed me to do so.
Why would you want to be sitting in one of the main cities for an hour waiting for that 1 tank to be logged on to do a certain instance? It bloody sucks and causes loads of issues.
Instead of being called a 'baddie' (I f^*king despise that term), you are held responsible for your own actions and deaths in dungeons which is far better than blaming the healer, dps or tank.
I can understand it will be hard to get your head around, but the 'Holy Trinity' system is pretty shit and you definitely don't need it to make encounters fun, entertaining and engaging.
EDIT: In addition, the mechanics of combat are different than any other MMO at the moment. Therefore, GW2's combat doesn't heavily rely on the trinity system, and instead uses the functions such as self heal, dodging and weapon switching.
I don't think anyone here is arguing for the trinity. In fact, the OP is an argument advocating its absence in favor of fun and interesting boss mechanics.