Interesting discussion. I am a bit on the fence, sometime villains work better with a back story, some times not - in the Jokers case I think Heath ledgers worked because it was a pure agent of chaos, (As Knox Noted, He Just Is) less man than force of nature, but as Karm noted Jack Nicholson worked for a different reason. As to this trailer, looks alright to me overall, but I'm happy to live with the idea of multiple Jokers with multiple origins, they all explore different 'possibilities' of the character in my mind, I might have a preference for Heath Ledgers version, but that doesn't mean you can't enjoy other versions.
As a general note on some other villains, i think the biggest mistake writers make is when a Villain (character like Hannibal or group like Borg) becomes popular they think this is popular lets use this more...and after initial 'fights' they end up being less enemy more Frenemy e.g. IMO Hannibal in the movie Hannibal/Red Dragon was far less antagonistic than Silence, Borg by the End of Voyager were an ally at time instead of relentless force. Exploring a back story is to me less an issue than 'friending' them as a method of keeping them going without the heroes having to destroy them outright.
To be Fair, Red Dragon came first...so It would be more he became More antagonistic. An Enemy teaming up with a Hero against a bigger villain is an old trope and one hard to pull off imo. On topic of the Joker...the Burton film gets away with a lot of "sins" because...well...its just so damn good. But I look at it as an exception. I too prefer the Joker being a bit ambiguous.
I could have done with less about the Xenomorphs and more on the Yatuja (Predators). Like Knox I read the comics and would love to see more of those stories adapted. Especially Bad Blood.