Your first sentence is partially right: Dark matter was born to explain a discrepancy. Unfortunately the rest is WAY off. The discrepancy had nothing to do with distance measurements. It was the fact that galaxies were observed to rotate faster than would be predicted by general relativity.
That leaves two options: either the galaxies have unobsevable matter or general relativity is not applicable to galactic rotations. Both ideas were considered seriously, but dark matter matches reality better than MOND (MOdified Newtonian Dynamics - basically the alternative to GR). MOND does better at explaining galactic rotations but does poorly when applied to larger scales than individual galaxies. DM does well at all scales. DM may be modified or abandoned as more data come in, but it’s not just a myth or a placeholder; it’s the best explanation for what we currently have observed.
Previously unexplained galaxy rotation was addressed with detection of giant black holes at the centers of galaxies.