I may have to respectfully disagree with you about MK's history being described as 'rich'; my sole disagreement being the folks at Midway can't seem to decide exactly how MK's history goes. I say this without intent for argument and with my tongue firmly placed in cheek, but please, if you would, consider and remember the following:
-The MK Armageddon Bio Fiasco -or- "Sorry guys, we forgot to do that part of the game before we began programming; here's a few bios to get you started and we'll leave it to you to imagine the rest of them." This is as close as I'll get to being flat-out pissed off here but as MKA is / was ostensibly the final game in the original MK storyline, leaving the bios out was kind of a slap in the face to those of us who stuck by MK from the beginning. As much as I support Boon and Co., I found this act to be inexcusable, intentional or not.
-The Scorpion As Sub-Zero's Guardian Arch: Scorpion witness Sub-Zero spare *someone* (it's never mentioned who), realizes this is Sub-Zero's brother and decides to be his guardian (MKII), continues to be his guardian (UMK3 / Trilogy) and then decides that he needs vengeance again (MK4). Yes, I know there's that argument of "Well, that only happened if Scorpion won MK II and he didn't, Liu Kang did" but that doesn't really hold water here: why would they mention it in UMK3 unless there was intent to do something with it? We've seen in all of the MK games that some endings are considered canon, regardless of who defeated the Big Bad at the end of the game. Scorpion needn't win MK II for his ending to be considered canon, at least until MK4 when Ed and Co. decided to retcon it entirely.
-Johnny Cage is dead (MK3), is alive (MKT), is dead but then alive (MK4). 'Nuff said.
-Raiden is a slightly arrogant thunder god out to show Shang Tsung how mighty he is (MK) who wants to stop Shao Kahn (MK II) who becomes the Mick to Liu Kang's Rocky by helping the scrappy Earthrealmers fight the Nazis and win the day (MK3 and upward) until the day where he fails to notice Shujinko being puppeted around by Onaga and decides vigilantism is the way to go (MKD).
-Baraka may or may not have been sliced in half by Kung Lao's razor-lined fedora but, it's OK, someone had some giant staples lying around to fix him (MKGold) and, hey, it was only a flesh wound; his body was patched up by MKD and never mentioned again.
-Cyrax is stuck in the desert (MK3) but can warp the fabric of space and time to spar with opponents while he's still stuck (UMK3). Schroedinger's Cyberninja perhaps?
-The original Mortal Kombat was a one-on-one tournament (MK1) but in actuality it was a free-for-all melee (Opening Cinema from MK Shaolin Monks). MK II was also a tournament (MK II) except for Liu Kang and Kung Lao who went on wacky misadventures in the plains of Outworld, occasionally fighting kombatants. Fact: Kintaro was defeated by Liu Kang repeatedly rolling into him and occasionally launching a volley of ki blasts / fireballs. Hand to God, I've seen it.
-When I mentioned Sub-Zero looking like George Clooney, I'm referring to how in his ending from MK II, unmasked Sub-Zero looks suspiciously like Josh Tsui (who may have written the book on Lightwave 3D but, I safely imagine, doesn't know martial arts on the level needed for motion capture in MK3) and he's flat-out played by John Turk in MK3 but the 3D render they used for MKDA and MKD looks more like George Clooney than John Turk.
Again, I'm not looking to argue, other than to say MK's history, such as it is, is far from a rich tapestry. Patchwork quilt is a little closer to home. I love every minute of it - C'mon, Mileena swallows a jar of nails? - but that doesn't mean I can't be critical of it, too. And, as I already said, if the story itself doesn't make a lick of sense, all that matters is the game being fun.