...how about giving examples of 1, 2 and 3-dimensional characters within the articles themselves?

That's what I call it when a writer creates a character with so much less characterization than their role in the plot that you could put a cardboard cutout in their place and nobody would notice the difference.

I'm not sure what the charge itself is called--perhaps an agent would call it "Forcing Generics into main-character roles", or just "bad characterization".

A notable example of a cardboard cutout from a Legendary is, of course, laura. She has no personality whatsoever, but is the main character in the story.

laura's amount of characterization would be appropriate in a well-written story only for a Generic--those characters in crowd scenes who never get speaking parts. She wouldn't even make a good bit character!

The Bad Psychology article touches on this: People have to act in consistent ways. Not necessarily rational ways, but your characters have to do the things they do because they are who they are. And if you don't know enough about who they are to figure out what they will do, then that's not enough characterization. The more they'll do in your story, the better you have to define their personality.

In the PPCverse, people who have bit parts in goodfic or canon are full-blown people. You only see small parts of their personality in the story, but it's all there. That's because good writing gives you the idea that whatever part of their personality you can see, it's part of a coherent whole. These characters are sentient in the sci-fi sense--full people whatever their species.

However, poorly-described badfic characters don't have a coherent personality or don't have enough of a personality to begin with, so they are more like cardboard cutouts than people. That's why most Assassins don't consider themselves murderers; they're not killing people, only crude facsimiles of people or distorted eldritch abominations that try to pretend to be people, but fail at it.

Many badfic characters try to shore up the rickety structure of their personalities by patching it with details. Instead of motive and identity, these characters have flowery physical descriptions, powers and abilities, or even trajeck backstories. But beneath it all, there's no actual person to be found.

That personality is a part of characterisation, but not the whole deal. I mean, take iconic weapons, for example. Off the top of my head, Cloud Strife's Buster Sword is a part of his characterisation, but isn't a part of his personality, per se. Ditto for Sherlock's deerstalker and opium pipe.