Because they liked both his star appeal and his acting for the role?
Superstar actors get to play whatever roles they want. They cast Kevin Costner in the very British role of Robin Hood, for goodness sakes. At least Downey did a decent job of maintaining the same accent on consecutive sentences.
This is a Hollywood film, and Hollywood is rife with, shall we say, culturally insensitive casting decisions to get stars in roles? That's well known as "whitewashing," so it get much worse than this. Mickey Rooney's Mr. Yunioshi from Breakfast at Tiffany's is the most famous and appalling example of this, I'd say. Christian Bale as Moses has been criticized, where Charlton Heston in pretty much identical casting wasn't. Times have changed.
However, here are examples of, not so much whitewashing, but roles where the actors are chosen to play roles not of their ethnicity.
- Brad Pitt as an Irish guy Devil's Own.
- Tom Cruise as an Irish guy in Far and Away.
- Any movie set in ancient Greece or Rome - British folk
- Any movie set in medieval times - British folk, or sometimes people with French accents
- Renee Zellweger as Bridget Jones..... three times!
- Many of the cast of Walking Dead, including Andrew Lincoln, are British.
- Alan Rickman (British) as German terrorist Hans Gruber in Die Hard
- Jeremy Irons (British) as Hans Gruber's brother in Die Hard 3
However, it's called acting, so, if the actor is up for it, it's not that big a deal, as long as it is plausible. The casting of Jonathan Pryce was roundly criticized as an earlier version of whitewashing when he was cast in the Broadway production of Miss Saigon. He's such a great actor, though, that he won many awards for that role. So, would it have been better if they cast an Asian in that part? From a purely entertainment perspective? Can you separate that, today, from cultural sensibilities? That makes for interesting discussion.