Neoclassical synthesis is still taught because, even though it's flawed, we have nothing better. Economists know that the assumptions behind neoclassical models aren't always fulfilled.

All science is always done with models and we just use the best models we have, while taking into account their limitations. People don't usually object to this in other fields, but in economics they do because they have stronger Opinions about economics than the natural sciences and the models sometimes disagree with their Opinions. If they had a better model, economists would welcome it, I'm sure, but they don't and they still want to keep their Opinions, so instead they blabber about how the current models are flawed. They're not wrong.

The Marxian school is a dead end and the Austrian school lacks scientific rigor. There's no point in teaching along with neoclassical synthesis things that are less rigorous than neoclassical synthesis while also having less breadth. If they were taught, the situation would be similar to what it is in psychology, where dubious approaches like psychoanalysis are taught alongside cognitive psychology.