So--first thing's first. Scientists know Dark Matter is not complete. Consider the progress we've made from the Copernican model of the solar system, to the Kepler model, to Newtonian gravity, to Einstein's theory of gravity. Right now, our understanding of Dark Matter is at the Kepler stage. We know what it's doing. We do not know why it is doing it.
But we have plenty of observations to lead us to what dark might be and what it definitely isn't.
Any theory of dark matter needs to explain all of the following:
1. The Virial Theorem, galaxy clusters, and the speeds of galaxies in clusters. (both MOND and CDM both do a good job of explaining this)
2. Galactic rotation curves. (MOND and CDM both do a good job of explaining this)
3. Accoustic Baryon Oscillations. (ABO) Immediately after the big bang, everything was ludicrously hot. The most powerful force in the universe was the wash of gamma rays everywhere. These gamma rays carried electrons around. The electric fields of the electrons carried the protons around. (the light dominated phase) As the universe cooled, this flipped; the protons were carried around by momentum, which brought the electrons with them, which mediated the light. (the matter dominated phase, where we are today) During the light dominated phase, sound waves pulsed through the universe, causing dense regions and underdense regions. When the universe flipped from being light dominated to matter dominated, these regions were frozen in time, and we can see them directly in the CMB. (cosmic microwave background) We can analyze the properties of these pressure waves to determine what the properties of the matter and light in the universe were. These waves demand some sort of dark matter. CDM explains these observations, MOND does not.
4. The Bullet Cluster. The Bullet Cluster is a collision of two galaxy clusters. We can measure gravitation lensing and light to determine where the dark matter is and where the regular matter is. The bullet cluster demonstrates that these two properties are not the same. There is matter which has gravity and gravitational lensing, but that we can't see. CDM explains these observations, MOND does not.
5. Ultra diffuse galaxies with very little dark matter. Not all galaxies have galactic rotation curves which require some extra sauce to explain the movement of their stars. Some galaxies are explained perfectly by the matter that we can see in them. So we need dark matter for most galaxies, but some galaxies need to be dark matter free. These galaxies falsify MOND.
6. Leading spiral arms in barred spiral galaxies. The large majority of barred spiral galaxies have their arms trailing from their bars, but a very small number of them have arms which lead in front of the bars. Computer simulations show this happens naturally with CDM, but MOND or dark matter free spiral galaxies don't have a mechanism to cause this to happen.
7. Gravitational waves travel at the speed of light. Most MOND formulations predict gravitational waves travel slower than c; all of those formulations are wrong.
There is a genuinely absurd amount of time, effort, and money that has gone into explaining dark matter. It is not a band aid, we haven't just added 1 to moved on. Everybody is pouring over every step of the algorithm trying to figure out why it's giving us the wrong answer. CDM is the leading hypothesis right now, because it explains all of the observations, and is not falsified by any of the observations. MACHO is/was another theory; it has gone out of fashion because it does not explain all of the observations and makes predictions we do not observe when we check for them. MOND is out of fashion because it is falsified by the data. MOND is still in fashion among a particular brand of people who just want to have their names in the history books; if someone did prove MOND, the history books would all have lists that go "Ptolemy, Copernicus, Kepler, Newton, Einstein, <your name here>."
But for Pete's sake it's not as if people have their fingers in their ears.
explanation of acronyms/terms:
1. Dark Matter. Dark Matter is the observation that the universe acts as if there's a lot more matter in it other than the stuff we can see. Basically no one says that Dark Matter isn't real; that would imply that the observations are wrong.
2. MOND. Modified Newtonian Gravity. MOND is a family of models which aim to explain the dark matter observation. Instead of using F=Gm1m2/r^2 to determine the force of gravity, we have better math, that gives a different equation, that accurately explains Dark Matter. When you say "physicists discover a much more logical explanation" that's what you're talking about.
3. CDM. Cold Dark Matter. CDM is a family of models which aim to explain the dark matter observation. CDM implies that Dark Matter is explained by particles. CDM implies there is some sort of particle of family of particles which interact with normal matter via gravity as normal, via the electromagnetic or strong nuclear force not at all, or via the weak nuclear force super weakly or not at all. CDM interacts with other CDM particles via gravity as normal, but only weakly via either the weak nuclear force or some other as-yet undiscovered force. People often use the terms Dark Matter (referring to the observation) and Cold Dark Matter interchangeably.
4. CMB. Cosmic Microwave Background radiation. After the Big Bang, the universe was opaque. Light would be absorbed by the stuff in the universe and then re-emitted. During recombination, the universe became transparent. The last moment of the various bits and parts of the universe switching from being opaque to transparent has the entire universe glowing in microwaves. This moment is captured in a snapshot, known as the cosmic microwave background. As we understand the CMB better, we learn a lot--a lot a lot--about the early universe.
TeVes (one relatistic formulation of MOND) predicts gravity propagation at different speeds than light. This is not a general result of MOND theories.