Just about every other RPG I can think of, aside from D&D or its clones, does the everyman better.
Really? I'm still not getting it. I build 'everyman' NPC's all the time. My game is filled with mundane NPC's who are consumed with the daily affairs and struggles of life. It's just that generally, most players aren't interested in playing those characters (and after a while, I believe I'd tire of running the low drama as well). They want to play larger than life heroes. But that doesn't mean that I couldn't run a game of mundane challenges under D20/D&D. In fact, most of last night (kick off night of the campaign) was consumed with mundane challenges undertaken (in extraordinary circumstances).
It's not just about having the characters mechanically represent "normals". It's about the way the challenges are presented to the group.
I don't understand you. What about the way the challenges are presented to the group is fundamentally different as the result of the mechanics between D&D and some other systems?
In DnD, the main type of challenge is an encounter. In just about every other game, the main type of challenge is a conflict (could be a encounter, could be something else).
Again, I'm not sure I understand you. I've played WEG Star Wars, Chaosium Call of Cthullu, GURPS, Gamma World, WoD, and Chill fairly extensively. I've a passing familiarity with Boot Hill, RIFTS, Amber, and Paranoia. I've read tons of other rules sets. I'm not sure that I agree that the main sort of challenges in say D&D and Call of Cthullu differ all that much. In fact, I play something of Call of Cthullu inspired D&D when I run the table.
D&D's paradigm/intentions for play are that "you are big badass adventurers".
Maybe. But you don't necessarily start as 'you are big badass adventurers'; you start as just barely above the ordinary 'mundane'. Your definitions are so broad that I'm not sure that they mean much. If you survive long in a Call of Cthullu campaign, you're certainly 'a big badass adventurer' if the narrative you've survived through is any indication. The main difference between the systems is mostly in how differently the two systems treat you as you become more and more removed from the 'mundane'. In Chill you start out as ordinary firefighters, emergency responders, photographers, professors, soldiers, and so forth, but you are also magically powered members of a secret organization that is saving the world. I don't see a big difference in the paradyms.
Traveler
Burning Wheel
Savage Worlds
Call of Cthulu
All Flesh Must be Eaten
Aces and Eights
and others I'm sure I'm not thinking of.
I'm not familiar with most of that list, but the one I am familiar with - Call of Cthulu - doesn't really do mundane any better than D&D, especially if you were to play 'D&D with a level cap' like E6 (or lower the bar however you like, E5, E3). I think part of the attraction of D&D is that it does play so well across such a large range of power levels.
I don't necessarily see the common trait you seem to see in the above systems. As best as I can tell, the common trait between them is that combat is lethal. But combat is plenty lethal in D&D at low level if you take the gloves off as DM. There isn't a single one of those systems that excels the body count of Gygaxian style throw the PC's to the wolves D&D. Also, if anything, because D&D is using a D20 mechanic (large range of fortune compared to the size of the starting modifiers), at low level, D&D characters are less compotent than starting characters in most other systems, especially if you use a more restrictive point buy in character creation (24, for example).
Again, the main difference is in how D&D by default escalates up from that to more and more superhuman challanges. But it wouldn't take a huge modification of the rules to prevent that from happening and just keeping the game low level, 'gritty' or whatever you want to call it. Nor would it be impossible to play a game with a slow advancement rate and a high lethality if combat is entered into such that the characters aren't ever likely to get out of 'mundanity'. Certainly I've seen 1e AD&D games run in that fashion.
It isn't what they have so much as what they don't have. They aren't shoehorning players into specific roles. That's a bonus, for me.
I still don't understand you. What do you mean by that?