What they're describing is well documented, but my understanding is that the reality is a blend of what you're describing and what they're describing.

To this day there's significant social pressure to not acknowledge how much racism and racial division played a role in them growth of suburbs in the US, but ultimately it's the documented history which is revealed to those who research the topic.

In many cases individual families were not overtly racist but they were caught up in the economic effects created by racist dynamics and felt they had no choice to go along. If property prices in your neighborhood are decreasing, because neighbors are leaving, and you have the means would you not feel compelled to leave to somewhere with rising property values? Real estate firms intentionally tried to create waves of fear to get people to rush to move, selling low, and then profiting on selling to newer Black families.

It was common for suburbs to have deed restrictions limiting areas by race, and for a while federal housing guidelines would not underwrite developments that did not racially segregate.

At the same time there were massive amounts of state & federal funding pouring into suburbs and highly disruptive unpopular overhauls occurring in cities while cities were also losing tax revenue. For people with the option the future of good living seemed like it was in the suburbs independent of segregation, but part of what fueled the frenzy was the racial segregation.

This has been written about broadly by social historians. This book, in particular, is illuminating: https://press.princeton.edu/books/paperback/9780691133867/wh...

Some other links:

https://news.iu.edu/live/news/24906-research-ties-persistenc...

https://www.apa.org/news/press/releases/2021/10/white-flight...

https://psmag.com/news/ghosts-of-white-people-past-witnessin...

There's also this rather infamous quote by one of the most powerful Republican strategists in the 80s, Lee Atwater: https://en.wikipedia.org/wiki/Lee_Atwater#:~:text=Later%20in...

I won't quote it here but it's very telling.

People also moved to suburbs in Canada, Australia, New Zealand and the UK.

Cars enabled people to have free standing houses and work became decentralised, which was also due to cars.

Many people prefer to live in a free standing house.

In places like Detroit racism was very much the primary reason in the 1940s, 1950s, and 1960s at least. Some of it was just personal racism, pure and simple. See "blockbusting" techniques used by realtors who would hire a black mother to walk down the street with a baby carriage to give the impetus for white people to sell quickly and cheaply. Or a black family moving into a house, the white neighbors trying to push them out via lawsuit for breaking a racially restrictive covenant, then losing so that all the white people left the neighborhood (e.g. read about Orsel and Minnie McGhee in Detroit, I was the primary author of the National Register nomination for their house).

The racist pressure to move was also a structural issue supported by the Federal government. Redlining meant you couldn't get loans to buy houses in certain neighborhoods, and those neighborhoods were exactly where black people lived. Literal walls could be constructed between two similar communities of different races so that the white side could be higher rated and have better access to loans (e.g., the Birwood Wall in Detroit). A ton has been written about the topic, I can't really do it justice, but the idea that people just wanted a bigger house was not the case. A lot of Detroit actually consisted of single-family homes with yards anyhow, so it was literally white people leaving a house for a very similar one.