If they aren't free parameters then why do we assign arbitrary dark matter content and distribution to galaxies like the bullet cluster/ultradiffuse galaxies with "too much/almost no/no DM" to "make it work out"?

If dark matter distribution weren't arbitrarily assignable, why would reputable physicists suggest that some galaxies might have a dark matter clump at the center and not a supermassive black hole?

The evidence for a highly homogeneous early universe has basically been refuted, unless systematic difficulties in assigning galaxy distances (certainly a possibility) JWST is observing galaxies that are forming WAY too early for a standard gravitational model; MOND has predicted early galaxy formation for more than a decade now.

> If they aren't free parameters then why do we assign arbitrary dark matter content and distribution to galaxies like the bullet cluster/ultradiffuse galaxies with "too much/almost no/no DM" to "make it work out"?

Something has to explain why galaxies aren't all exactly the same right? Whatever other theory out there will have some "free parameters" that explain that difference won't they? The observable matter differs, why shouldn't dark matter?

I think you're being really cynical about the scientific process here. The process is a new observation comes along that's a bit out of line with the norm and scientists look at the parameters and see if Dark Matter is still a candidate to explain it. Do you think it's unrealistic to assume that different galaxies might have different amounts of dark matter (should it exist)? They have different amounts of observable matter. If there was some galaxy that just didn't make sense by just adding some arbitrary amount of dark matter, it'd put a real damper on the theory but that hasn't happened yet. As of today, the only thing that seems "off" about galaxies is the amount of gravity which is very simply explained by adding in some amount dark matter.

I think my intuition of that is probably the same as your, that it seems kind of ridiculous to just add some invisible matter to the equation but it does actually do a really good job of explaining a few different phenomenon. I suspect the process for the acceptance of dark matter initially began as a "these galaxies are behaving _as if_ they had more matter" and a lot of people trying to explain why that might be to no avail until they kind of just accepted that maybe there just _is_ more matter that we don't see. At least that's how it's been for me. I'm still holding out some kind of hope/expectation that there's a better theory out there that actually explains dark matter/energy in a more satisfactory way.

It's not rediculous to add invisible matter. This is how we discovered Neptune, and Uranus. But it didn't work for Vulcan and Pluto was super sketchy. But to scientist's credit they gave up on dark matter Vulcan when nothing was found, over and over again, and GR explained mercury's orbit.

The analogy would be if we didn't figure out GR, used dark matter to explain mercury's precession, then used dark matter to explain aberrant voyager probe kinetics, then rejected GR because "it failed to explain the weird motion of voyager"

Adding invisible matter is not crazy, but over time you make your model increasingly unfalsifiable as the observations fail to meet the expectations. Ideally that would decrease confidence in the model, but for dark matter it seems to have entrenched the conviction of mainstream astro.