First it was assumed that Newtons laws of celestial motion applied everywhere, but this was contradicted directly regarding galaxies.
Actually, we knew Newton's laws did not apply universally. It was expected that they would apply in the case of galaxies because of the low velocities involved.
Following the scientific method strictly, this should lead to a revision of the law,
No, it requires that we revise our understanding. There are two main ways to do that: change the law itself or hypothesize something extra. Both ways were tried with galactic dynamics (MOND and dark matter). But it was found that even if you change the law, there is still a requirement for dark matter.
One possibility that has arisen is that the assumption that Newton's laws are a good enough approximation for galactic dynamics because of the low velocities may be wrong. It seems that the non-linear aspects of general relativity might explain some of the observations. In essence, the relatively strong gravitational field in galaxies might be enough to explain the observations. We shall see.
but they just invented another assumption to the first one and now lots of other assumptions have followed all around in the observable univers.
This is no more an assumption than the hypothesis that a planet was producing the effects on Uranus. Using Newton's laws in that case lead to the discovery of Neptune.
Another example: conservation of energy was seen to be violated in certain weak reactions (beta decay). In 1930, Fermi postulated an unseen particle, the neutrino, to explain these observations.Neutrnos were first detected 26 years later.
This is not science, but science fictions and pure hindsigth bias speculations.
Actually, it *is* science. It is perfectly in line with how science does things: investigate ALL possibilities and choose the one that fits the observations the best. In this case, the basic law was preserved and an extra type of matter fit the data better.