All you have to do to know that a modern Mandarin would work is watch Arrow. Nyssa Al Ghul, eastern assassin dragon-lady, one of the oldest stereotypes from the old pulp 30's stories, and yet she's awesome. That's the truth of a lot of these old pulp stereotypes: they are inches from being awesome.
Iron Man 1: Worked with Iron Mongor to buy weapons and kidnap Tony.
Iron Man 2: Gave Ivan the fake passport to help him.
Black Widow Strikes Comic: Trying to use the missile to strike North Korea, create conflict.
Iron Man 3 Preclude Comic: Attacking various places, maybe set the trap to scan War Machine.
Iron Man 3: Name was used by A.I.M to cover the explosion, but maybe it was part of the Ten Ring's plan, using AIM to switch the focus of the SHIELD.
All Hail the King One Shot: Kidnapping Trevor because the real Mandarin was "angry" or perhaps, use Trevor for some sinister purpose.
Marvel really spent a lot of effort on this organization, almost all the crimes in the Iron Man movies had something to do with them, hope we won't be disappointed in their future storyline.
Just watched it. A good attempt from Marvel to redeem themselves after the "actor Mandarin" thing. But it is just that, an attempt to redeem themselves. No way they're going to use it in the future movies or include the real Mandarin anywhere.
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Azula: My mommy didn't love me so I'm going to burn down your village.
Don't you Quanchi me, mister!
Think about it. How many people watched this one shot compared to how many watched IM3? The build up for Mandarin Kingsley was greatly done but they screwed up near the end. And now they're supposed to start anew with another Mandarin? Make him a threat again and have people buy it? "Look! We have another Mandarin but this one is real deal!" Sounds too soap opera IMO. Don't think the audience will like that, except for those who read comics.
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Azula: My mommy didn't love me so I'm going to burn down your village.
They could just explain it in a movie, saying he escaped with unkown help or whatever. And then show us some scenes of where he is now.
So that's not much of an issue (except for what you said about audiences saying wtf is this now). But I'd say the bigger issue is when would this new Mandarin come along. There's not planned date for the next IM movie yet, and chances are Downey won't be in it. So unless they continue the plot in Avengers 3? But I doubt that will happen.
I'd say more chance of it being explored in Agents of SHIELD or something. But then what's the point in that now?