The vast majority of RPG characters are not even well-rounded enough to become two-dimensional, to say nothing of three-dimensional.
A quote from Pulp Hero on the topic that perfectly encapsulates my nearly 40 years of experience gaming.
“Hand-in-hand with the “action” convention is the fact that Pulp characters are shallow, clichéd, and poorly developed. In an action-oriented story, there’s little (if any) time for the hero to ruminate about how he feels, or what the events in the tale mean to him; he’s got things to do! Even the best-known Pulp heroes — characters like the Shadow and Doc Savage about whom hundreds of stories were written — aren’t much more than collections of easily-identifiable personality traits, quirks, mannerisms, and habits, possibly coupled with one or more distinctive elements of appearance that makes them easy to write and read about.
This is the other thing that makes Pulp so wonderfully gameable. The description of Pulp characters given above could apply word-for-word to the vast majority of gaming characters. Most roleplaying games, including the HERO System, require you to create characters through various attributes and traits defined by the rules. It’s a more elaborate, and sometimes “scientific,” process, than how a writer for the pulps worked, but the end result is the same: a character who’s really not a character so much as he is a characterization — a collection of traits that identify him and let him take action, and not much more. In short: RPGs are ideally suited for creating Pulp-style characters.” (Pulp Hero, p10)