Dark matter as a particle has to have certain properties in order to satisfy what we know about a) it's EW interactions and b) the fact we haven't seen it yet.

Over the next 20 years or so we will likely cover a huge amount of the phase space of direct observation of dark matter like candidates assuming they weakly interact with the standard model.

If we observe it, great we now know a huge chunk more than ever before of the universe.

If we fail to observe it then we have to go away and explain the Dark Matter problem another way. Axions are my personal favourite here because I claim nature for her beauty is sometimes horrible. But this could (in the most scary scenario) potentially be non quantisable interactions between unknown aspects of the universe. At that point we need to further our understanding of potential graviton candidates to evolve our theories of spacetime.

DM isn't a solid prediction like an aether it's a statement of a big gap in our knowledge that has implications to asto and particle physics models.

The big problem is then CP violation (why more matter than not, real why are we here at all stuff). This can't be explained by the standard model and stuff we can see and touch as far as we know. So we assume that this huge amount of it that we can't explain must come from interactions with new particles somewhere in some way at some energy scale.

Physicists try to narrow down that phase space of where and how but a lot of this stuff makes the search for the higgs, look like cheating and watching where your parents hid the Easter eggs. There is scary little to directly go on so theoreticians have to get clever.

Edit: There is also little to say that extra-SM CP violation _must_ be from the same source as Dark Matter astro candidates. The combination of the 2 fields is much more a car of. "Hmm we both have a missing piece in our jigsaw that has 3 of the same sides and a 4th we've never seen. That's odd let's look together to try and find it." Modeling of the early universe to today relies on some unknown amount of CP violation occurring and we know we see it in particle physics which describes everything we see eat and touch. So why the amounts are so different (orders of magnitude different) keeps some scientists up at night.

The idea is to propose a model that does not need dark matter to describe observations.

Unfortunately a lot of the models try to remove DM completely from either a gravity or CP perspective and both have direct consequences as to what sort of stable structures in the universe that allow to form. And the models often conflict with other observations showing theyre no better.

It's asif Newton observed an extra solar comet and therefore decided the Principia must otherwise all be wrong. It's a big step to say shinny thing in sky makes the Apple not fall as we observe it.