What you may be missing is that in the US starting around 1950s, suburbanization inverted this millennia-old globally-generalized pattern. It was called "white flight" [1] at the time, because richer mostly white workers moved their tax revenues out of the city limits. Because so much infrastructure and social structure (like schools) was funded largely or even entirely from the local tax revenue, it hollowed out the "inner cities" and the feedback loops were devastating. That's why New York City became the murder capital of the world in the 1970s. Colloquially, in the US, "inner city" [2] came to mean a low-income and mostly minority neighborhood full of crime, not anything specific to its geographic location.

[1] https://en.wikipedia.org/wiki/White_flight

[2] https://en.wikipedia.org/wiki/Inner_city

Definitely (I’m an African American who grew up in “inner-city” Sacramento). There’s been a reversal of this trend during the 2010s, where the inner city has seen an influx of higher-income residents seeking lower home prices and shorter commutes. Places in San Francisco like the Mission District and Hunter’s Point have undergone significant gentrification. However, low-income renters in the inner city have been unable to keep up with rent increases, which has resulted in an exodus to exurbia or to entirely different metro. I have relatives who moved from Sacramento to Bakersfield for a lower cost of living. There has been a “reverse Great Migration” of African Americans from the inner cities of the North and California to large Southern metro areas such as Atlanta. Some of my relatives have “returned” to the South after three generations in California, albeit not to the same Southern communities or states their grandparents lived.

it's also worth noting that one big contributor to white flight was the desegregation of schools.

Big city school systems would now have to integrate people of color with white children. There were plenty of people who did not want this, and unscrupulous realtors would use blockbusting to generate huge profits, where they basically scared white people into fire selling by telling them minorities would come into their neighborhoods and integrate their neighborhoods, and then turning around and selling to minorities at inflated prices. https://en.wikipedia.org/wiki/Blockbusting

Suburbs were effectively havens for white people since most minorities could not afford to move into suburbs, and their separate school systems became effectively all-white as a result.