But if you throw is dark matter and have it influence the other matter... Shouldn't the regular matter influence the dark matter too? At that point doesn't it end up in the same distribution as the regular matter? And isn't it then just unaccounted for? And wouldn't it have zero effect on the shape of the rotation curve?

I've seen reports of "fixing" the problem by assuming a galaxy is enclosed in spherical ball of dark matter. But of course no explanation of why it would maintain that shape. In other words, the model of dark matter isn't even complete. In some cases I've seen people misapply the divergence theorem as well.

It would not be the first time people used a hack to "fix" what ultimately boils down to numerical problems or inadequate integration methods.

Somewhere down my bucket list is to do galaxy simulation. So far all I've done is plot rotation curves that don't look like keplers laws, but no dynamic simulation yet.