For example, in a more realistic scenario people move for all sorts of reasons: leaving parent's house, changing jobs, marriage and divorce, etc. This stirring may lead to decreased segregation for slight decreases in bias, unlike what this more static model suggests.
The article is just showing why segregation is possible even if people have a very slight bias towards being near people like them. It doesn't prove this is the reason that any place is segregated, and it doesn't attempt to emulate every possible reason why a place would or would not be segregated.
In fact, at the bottom of the article you can see it says Schelling's model is a convincing demonstration of how innocent-seeming rules can create very undesirable outcomes, but of course real-life situations are more complicated. You might enjoy taking a closer look at real data in reference to Schelling's model. W.A.V. Clark's 1991 paper Residential Preferences and Neighborhood Racial Segregation: A Test of the Schelling Segregation Model has a lot of interesting data in it.
If you want more complete answers, look at that. This article is just demonstrating one concept.