Looks like a hell of assumption to make about stellar density. We know the cores are way more dense than the rest of the star, that's the magic that makes the fusion happen.
Now if this assumption is qualified and addressed later in the paper, I'll be guilty of not being careful enough, but I haven't found that clue yet.
That isn't a bad assumption to make. Take a star with spherical shell density proportion to 1/r^3. Perform a scale factor transformation to r* such that the spherical shell density per unit length is uniform for the new scale factor. Solve for the quasistatic collapse of a uniform density star. Perform an inverse scale factor transformation on the collapsed uniform solution. Nothing wrong with transformations to make the math easy. Solving for a simplified case sometimes makes solving a less trivial case easier, so long as there is a simple relationship between simple and complex cases.
Also, a simplified case places constraints on the solution for a more complicated case. The density of a spherical cow is the lower bound for the density of a non-spherical cow.