The US is only really diverse if you reduce everyone into a paste and spread that paste evenly across the entire country. You look down at the level of counties / cities / neighborhoods and the US really isn't that diverse. Which on the one hand is discouraging, but I think you could also argue the US has never really tried actually having diverse communities, and that that therefore could still work.
I'd say in comparison to a lot of other Western cultures we are pretty diverse - having been around in Europe, while racism is perhaps much more subtle and not nearly as violent here, the population definitely tends to be much more homogenous. I think it probably comes down to the fact that there is no such thing as ethnically American unless you're Native American, whereas other countries have a strong sense of ethnic nationality.