I think that as it's presented, the authors are suggesting that it's a model that is necessary and on some level sufficient to understand the dynamics of self-segregation in housing.
They subtitle the post "This is a story of how harmless choices can make a harmful world." Reading it, I get the powerful impression that the authors think that this model has the basic answers for all self-segregation in housing.
But obviously an even slightly more complicated model undermines many of their points. Like, they make a big deal of the idea that if you have a fairly high level of "shapism" and thus get a fairly segregated society, and then you lower the level of "shapsim," nothing changes unless you actively reverse your bias and move if your neighborhood is not diverse enough.
But clearly people don't only ever move for diversity reasons. Sometimes you move because you got a job or a SO that's far away. Sometimes you move because you can afford more or less living space. Sometimes you move because you have a child now and want to get into a good school zone. Or whatever. And if your preferences are now, compared to when you last moved, more tolerant, that WILL reduce the level of segregation of your society.
In fact, people probably move for economic or family reasons far MORE often than they move for diversity reasons.
I mean, that's not a small difference from their model. It's one of their major points! That, once segregated, societies won't become less segregated unless people actively work on it.
And, honestly, I don't think that the model holds at all unless you understand that people probably mostly use economic proxies for race over primarily making decisions based on race. For the most part, I don't think people are saying, "I don't want to move there, there's too many black people." They're saying, "I don't want to move there, it's too poor or too crime-ridden" or whatever. And yes, they may be exaggerating the extent to which it is poor or crime-ridden because they have internalized racist ideas about whether majority-black neighborhoods are poor or crime-ridden. But the point is, you can't really address this segregation by telling people to prefer mixed neighborhoods: you need to address the complex relationships of economics and race and how economic class affects neighborhoods and whatever.