Jagar Tharn. Dagoth Ur. Mankar Camoran.

All attempted a wild upset, tried to change the game.

And they all failed.

Because they lacked The Three: Mage, Fighter, and Thief

Recall all the successful revolutions on the timeline. The events that reordered the cosmos, laying Aka out on his back.

They succeeded. They had The Three.

Creation of The Mundus?

Magnus, Akatosh, Lorkhan.

Foundation of the 1st Empire (and/or "Freedom")?

Pelinal, Morihaus, Alessia

Establishment of the Tribunal?

Sotha Sil, Almalexia, Vivec

Foundation of the Tamrielic Empire (and/or Talos)?

Zurin Arctus, Wulfharth, Tiber Septim.

Perhaps those archetypes have some deep metaphysical resonance in the Aurbis. Maybe goals are just better furthered with a group possessing a diverse skill-set. Whatever the case, they're certainly pervasive enough.

Now that you point out the recurrence of trinities, its certainly interesting.

One could poke holes though - Mankar Camoran had his son and daughter by his side during the final confrontation.

None of those break down into clear D&D archetypes, with the exception of the Tribunal (which is itself upset by the fact that the Thief is also a Warrior Poet and the Warrior is also a Mother). I also wouldn't say that Mankar at al failed. They didn't achieve as radical a change as they thought, but they still had deep impacts on the future of Tamriel.

We have trinities (the Enantiomorph and the Anuad come to mind), but they aren't quite that clear.

It is a very interesting thought, when put together in that manner. Perhaps since such a trinity embodies the three basic ways in which any situation can be solved, it could be said that those who embody that trinity have all their sides covered, and thus higher probabilities to win, since they are prepared for mostly anything.

Or something.

I've always thought that those three archetypes were important to TES. The stars themselves are evidence.

True. But weighing them against the stellar success of Tiber Imma-Get-Ridda-Dis-Endless-Jungle-For-Y'all Septim, they fall rather short.