All that is true. But there's also the issue of Red Lining and race-based lending practices and real estate shitfuckery that make certain neighborhoods - which would otherwise be affordable to everyone in the given income bracket - inaccessible to PoCs. This, combined with staunch refusal to adopt multi-lingual education (particularly the dreaded Spanish), and segregation of education (whites-only Universities), and segregation of career paths (engineering firms and legal firms and hospitals/clinics that won't take on junior hires outside their ethnic group), force people to cluster together by circumstance.

This doesn't even need to be segregation by income, either. Houston's Bellaire district is overwhelmingly Vietnamese (and South East Asian generally speaking) in large part because its the only part of town that caters to Vietnamese non-Native speakers. There's no shortage of wealth and even some amount of political power consolidated in Bellaire, but its still functionally a ghetto.