You are quite correct that the Oppenheimer-Synder model assumes a non-interacting (pressureless) dust, and that means the dust will inevitably collapse into a point mass. The value of the model is not that it's a particularly realistic model for real collapsing stars, but that it captures the main feature of a collapse.
For example the OS metric tells us that the event horizon appears at the centre of the collapsing ball and grows outwards until it has grown past the outer edge of the ball, at which point it becomes static. We expect this to happen in real collapsing objects as well. The details will be different but the overall process will be the same.
We can use the OS metric to find out what happens to an observer falling in with the dust and one watching from far away. Have a look at my answer to Does an expanding event horizon "swallow" nearby objects? where I describe this. Again for a real collapsing object the details will differ, but in general terms we expect the same behaviour.
Exact solutions are few and far between in general relativity, and none of the exact solutions are a perfect match to reality because they all involve simplifications that we have to make to get the exact solution. This applies to the Schwarzschild and Kerr solutions, and it also applies to the Oppenheimer-Snyder solution. But studying the properties of these solutions can give us a lot of useful information for doing numerical calculations of more physically realistic systems.