Due to min/maxing, it's usually not possible to replace.
Very few games found ways to replace it, but usually via hybrids who were able to be multiple roles equally as good as those who specialize. (Looking at FFXI BLM burns. BLM use Control, to avoid dmg intake. Use strong burst dmg spells, timed together, and they usually had healing spells slapped on from their cross class abilities.)
To the OP.
Am I tired of it?
I like being a tank.
I like being a healer.
I like being a DD.
But I am kinda tired of seeing the same thing over and over.
I've seen the argument ppl can't be equal, and dependent, because it takes away difficulty. (Not really, Ninja Gaiden can be considered really hard, but you can be sure to beat the game w/o a healer. You can argue different game doesn't apply, but it does, if you understand HOW a game can be hard. (Needing perfection))
Though my issue with the trinity, is mainly to do with how useless 1 of the 3 are...
Every MMO that has these 3 roles, DDs become the favored role, either due to lack of responsibility, or for the joy of competing with other DDs DPS. (Other factors kick in as well.)
WoW and other MMOs, eventually realize they needed to give a REASON to have DDs. Otherwise like FFXI, you can stack a team of healers and tanks, and win a fight by turtling. (Not that there shouldn't be such fights, at least for variance.) So now most MMOs either make time limits at the start, or later realize they need to add them. (Be it actual timers, enrage timers, or non returning MP.)
Now it seems like the "teamwork" is more about competition, rather than cooperation.
You and the tank want that oh so good gear? You only work together, for the common goal, but in the end, you don't want the other to win.
The trinity is designed to hurt each other.
DDs CC for tanks, tanks help the healer not run out of MP, and the healers help the low defensed DDs alive.... BUT NOW....
DDs need to keep dmg up, in order not tpo run out of time, which pulls threat.
Tanks need to stop using as much defense, in order to hold hate over the DDs.
The healer needs to heal the tank more, because they aren't keeping up their defenses.
Is this a challenge? Of course.
There's nothing wrong with challenge, BUT! there is something wrong with turning your teammates against each other, and creating the cesspool known as WoWs Random Dungeon Finder.
Of course the fix is get a guild, where this stress is usually ignored, all for the sake of over coming the challenge of it.
Now that I explained my issues with the trinity, the sole goal to an MMO is teamwork.
No matter how we slice it, relying on another person can apply stress to both parties.
Which means there is no real answer. We just deal with it.
So looking back, the most popular roles are DDs... and what benefits can they get? Their high DPS is only interesting because of their competitive nature, lack of responsibility until endgame, or quicker kill times solo.
How can you make them better suited as teammates, who work together with the group? How do you make the tank and healer roles equally appealing?
Most people will argue "Hybrids!" But there IS another answer. (In fact MANY more answers!)
But the ONLY way these alternative methods can work, is using a new system, from the ground up, rather than just copying UO or EQ, and slapping on a new trinity or w/e.