I don’t think America is particularly worse than most places on this.
Playing a real life or established character is an exception of course but in most cases race and ethnicity doesn’t really matter, gender too at times, Hollywood actresses have started pushing to be cast in scripts with male leads and getting that detail changed. That’s the approach Shonda Rimes takes where (unless again it may be a family member of an existing character) they don’t set any ethnicity in the scripts and then just cast the best actors.
It certainly doesn’t matter for ‘Sky’ in Agents of Shield, I wonder how many parts Chloe has taken where her mixed heritage causes any story issues at all? Probably none of them, so it’s sad it becomes one.