Why should it be the goal of the law to hinder prosperous but ethnically homogenous areas? Personally I like my diverse neighborhood, but I also like that Chinatown is just down the street.
Because the reality of racial restriction covenants and redlining practices is that they weren't used to develop great locales; they were used to systemically exclude people of undesired races who otherwise had the means to live in said area.
This doesn't mean that ethic areas just melt away, though. Chinatown can remain Chinatown on the basis that they value being close to Chinese community centres and Chinese grocery stores more than the average resident, meaning they're willing to pay more and price out other people to live there. They can't remain Chinatown by literally refusing to rent to someone because they're black, though.
This allows ethic areas to remain if they provide a benefit to their community, but melt away to redistribute real-estate resources more efficiently if they don't.
isn't the point of things like rent control and affordable housing to specifically prevent people from paying more and pricing out people who want to live there?
It comes down to this issue of whether or not more housing is available. In New York, there's effectively a finite cap on housing, so you can't just say "well buy somewhere else". Pricing caps and assistance programs make sense there, but those also come with less ability to control your neighborhood.
When there's tons of cheap housing available, then having small areas with expensive pricing isn't per se a problem (but could be an issue in context, say a small midwestern town excluding black people from buying houses by over-inflating prices.)