The idea of villainous archetypes certainly isn't new, or unique to comic books. But when part of your central schtick is "one hero with many foes", then devices that help distinguish those foes become useful. Conceiving of archetypes among villains then helps you create new ones: you can see where the "gaps" are in the hero's villainry and create a character to fill it.
This concept is similar to the Dynastic Centerpiece Model we talk about here. In the DCM, we find patterns between a Dynastic Centerpiece and his or her helpers and supporting cast. In what I will call the Villainous Tarot, there's a set of archetypes that DC villains fall into it, in which, like the Dynastic Centerpiece Model, the members are defined in terms of their relationship to the central hero. The more fully that "Tarot" is filled out, the potentially richer the hero's Rogues' Gallery is.
Filling out the Villainous Tarot isn't a sure-fire thing. If you fill it with crappy villains, then your hero will still have a crappy Rogues Gallery. BUT-- and here's the key thing -- quantity (or, more accurately, variety) is more important than quality. More on that later!
But first, let's take a look at a sample for the Trinity...
|Crime Lord||Penguin||Lex Luthor||Veronica Cale|
|Opposite Number||Killer Moth||General Zod||Devastation|
|Twisted One ||Two-Face||Bizarro||Silver Swan|
|Mental Challenger||Riddler||Mr. Mxyzptlk||Dr. Psycho|
|Physical Challenger||Killer Croc||Parasite||Cheetah/ Giganta|
|Sexual Challenger||Catwoman||Maxima RIP|
|Evil Genius||Hugo Strange||Lex Luthor||Dr. Poison / Egg Fu|
|Manipulator||Mad Hatter||Dr. Psycho|
These are just some of the more obvious villainous archetypes. They aren't mutually exclusive (one character may fill more than one role) nor unique (one role may be filled by more than one characters). Nor is there any necessary hierarchy among these archetypes; for various reasons, a hero may wind up with an "archenemy" who's a Mocker (the Joker), an Evil Genius (Lex Luthor), or an Opposite Number (Zoom). Nor are these roles immutable; villains can evolve from one role to another (as Hugo Strange once evolved from Evil Genius to Opposite Number or Twisted One) or occupy different roles as the situation demands (e.g., the Penguin as Gadgeteer or Crime Lord). Role can be usurped; the attempt to create Devastation as an Opposite Number for Wonder Woman didn't stick long-term, and the new "Super-Manazon" that DC appears to be planning will now take that role instead.
And this is why the variety, overall, is more important that the quality. Quality is easy to fix. If a villain in a particular role is crappy, all it takes is one issue to give them an upgrade or make them more interesting. As long as a villain has any recognizability, they can be given a new paint job (e.g., Catman, Egg Fu, Black Hand). It's harder to introduce new villains and make them stick than it is to revitalize them.
When I asked you to come with an "anti-Trinity", you each chosen a different set of villains, and, consciously or not, your choices were influenced by what role the villain plays in that hero's Villainous Tarot. Some of you chose villains with the same role, so that they would all have a common goal to give your team unity. Some of you, on the other hand, chose villains with three different approaches to give your team variety. It's like in Risk, when to get extra armies you can turn in either three of the same card, or one card each from the three different types. Re-examine your own choices with the Villainous Tarot in mind, and see what it tells you!
Just like the Dynastic Centerpiece model, the Villainous Tarot can highlight weaknesses in the mythos of a hero. Try filling in the grid above for another hero. The problems are immediately apparent. Most of Flash's villains are, essentially, gadgeteers (and one trick gadgeteers, at that). Small wonder, then, that they've largely been lumped together what amounts to one threat with a variety of faces ("The Rogues"). No one's taking the role of the Mocker of Green Lantern (except for, you know, me and the rest of the internet). Black Manta has to fill five or six slots in Aquaman's tarot, and if you want to have a serious laugh (or a serious headache, depending on your attitude) try and fill that grid in for Green Arrow or the Martian Manhunter.
The nice part is that, in pointing out gaps, the Villainous Tarot spotlights opportunities. As previously mentioned, somebody at DC obvious thought something along the lines of, "Hey, Batman and Superman each have at least Opposite Number, maybe more; shouldn't Wonder Woman have one, too?" Angle Man's not really Wonder Woman's Mocker, just the closest she has to one; he could be pushed more in that direction, and new villains could be placed in his original roles as Mental Challenger, then Gadgeteer. Wouldn't someone Grimbor-like be an amusingly ironic foe for Wonder Woman, perhaps as an enslaver of trafficked women? Or old villains could be re-purposed to fill those roles; wouldn't Circe be more effective as a Mental Challenger for Wonder Woman, rather than as a tepid Mocker of her values?
The specifics of what is done what role or which character are merely details, and you could make a wide variety of interesting and valid choices. I wouldn't want to see every hero's Rogues' Gallery become cookie-cutter predictable, but I would like to see writers and editor take greater advantage of some obvious opportunities to fatten up their hero's Villainous Tarots!