I guess what is different about dark matter is that it has to outmass regular matter by a large factor. It feels unparsimonious to invent four-five times the mass of the known universe just to patch a discrepancy between observations and a theory of gravitation. It feels like the theory would better be adjusted to match observation than to patch observations to match theory.
Today I learned that the mass of the neutrinos we know about (which were similarly invented, though since detected) about matches the mass of all the stars.
Actually, in the context of astrophysics, that exact objection has been employed many times. For example, the most famous argument against heliocentrism was that it would require the stars to be ridiculously far away and ridiculously big to patch away the lack of parallax, which felt unparsimonious. Similarly, people believed that galaxies weren't galaxies, because it seems unparsimonious to expand the universe far beyond the Milky Way just to patch up some weird features of fuzzy nebula. And even in our galaxy, the mass in dust and interstellar gas exceed that in stars.
Literally all progress in fundamental physics is "just" "invented". Each time it must triumph against the objections of the same, thousand-year-old philosophical arguments.
Today I learned that the mass of the neutrinos we know about (which were similarly invented, though since detected) about matches the mass of all the stars.