> ...so far nobody has figured out to socially engineer that outcome

Isn't forced busing a counter example? When I was younger it increased my exposure to different races and expanded my friend groups. By the 90s my family had moved a few times and the bussing had ended nearly everywhere. Things were far more 'naturally' segregated without some forcing function.

Coworkers with similar bussing experiences said their friend groups were also more diverse than peers or younger generations who didn't have it.

Civil rights legislation (and enforcement) also ended phenomenon like whites-only businesses and bathrooms. Changing some centuries old racism may just take longer than we expect.