I fear that the omission of the "holy trinity" will end up hurting the game in the long run, while it works for the most part I truly believe that part of an mmo's success is attributed to dungeons, especially at the end game level.
With no clear tanks or healers all dungeons will be delegated to a Zerg fest.
Also With lacking threat management and not being able to be an effective tank in the group melee dps is almost always screwed due to the fact that the boss will just turn on you at any given moment and mess you up.
In the end the unstructured over dungeon scenario will be the downfall of this game for me, however as of now in the leveling and exploration process Im really enjoying the game.
It's sad they really did a lot of things right here, just a few things that I feel while trying to differentiate from other mmos will end up driving mmo players back to that other game in the end.
I experienced this as well, however I think that right now dungeons are only so unstructured because not enough people know enough about their class to really know how to perform in a dungeon.
For instance, if this game had a holy trinity the dps would generally know that they needed to be pumping in dps, the tank would know they need to be the one keeping the dps from getting hit and the healer would know that they should be running around making sure no one dies (lets forget whether they're any good at it for the moment).
However, this game has blended the holy trinity into each of the classes and made each party member accountable in some way for each role (albeit in varying amounts), so it has become more difficult for each party member to know how best they can support their team. Unfortunately, this means that most people will just give up thinking and do random things while hoping for the best (i.e. zerging). But over time I expect as people get more used to what their classes can do it will become less of a zergfest (at least for static groups).
I think what will happen eventually is that people will learn that "tanking" is no longer a 1 person job, but instead a group effort where 1 person might hold a enemy's aggro, but everyone else will be watching the boss' movements to use their support skills (when necessary) to prevent that person from taking too much damage. i.e. a guardian who does not have aggro currently will notice the current aggro target is out of dodge points, and so casts his/her aegis to protect the aggro target from the next attack, later on the party's engineer might be able to help out by knocking the enemy down or blinding the target, etc. etc.
I think a gameplay dynamic like the above could prove to be very interesting for all party members and much more engaging for the party as a whole than the holy trinity is. However, of course this is just speculation from theorycrafting, but nonetheless it will be interesting to see how it works out as the game matures.