Why do we think that the dark sector is simpler? Matter makes up roughly $5\%$ of the Universe while dark matter makes up roughly $25\%$. For matter and radiation, we have a complicated Standard model with many generations of fermions and various force mediators. Given this fact isn't it a wishful thinking that dark matter is made up of only one particle? People try that because that's the simplest thing to try.
But in absence of any definitive observational or experimental signature how justified is that simplified version of the single component dark matter models?
 A: One of my favourite dark matter theories is mirror dark matter: the entire dark sector has exactly the same physics as ours: there are dark electrons, dark photons, dark protons etc interacting with each other. This is exactly as complex as our physics. However, the theory then needs to find a creative way of explaining the relative smoothness of dark matter halos compared to our galaxies (basically lots of supernovas keeping it mostly plasma). This is conceptually simple, even though the dark matter world is/will eventually be just as complicated as our world. 
(I don't actually believe there is mirror dark matter, but it is a fun concept and illustrates my point.)
The problem here is that "simple" is not a simple concept. It might mean that we want to use the theory that adds the fewest extra things - but does that refer to extra laws of nature, extra symmetries, extra particle types, extra interactions? It might also mean that the overall theory should be as little arbitrary as possible - each extra thing should ideally fit or explain as many unsolved issues as possible (this is why we assume dark matter is behind both galaxy rotation curves and cosmic structure formation rather than assuming two separate unknowns). Mirror dark matter does pretty well on the first approach, just double physics, but it does not do that well on the second since there is little new explanatory power. Axions were proposed as a solution to another problem but could also be a dark matter candidate, so they do much better on the second meaning.
I assume one important constraint on dark matter complexity is that back when the universe was hot enough presumably matter and dark matter interacted, and the number of degrees of freedom of the dark matter would have affected baryogenesis and other properties of the big bang we can today measure. If there was a zillion degrees of dark matter freedom that would have left a thermodynamic mark on the universe.
A: Why do we keep dark matter models simple? It's partly because science progresses best if, when we realise current theory is missing something we try the simplest way to address that first; if even that turns out to be empirically wrong we can add further complexity, but if we add complexity prematurely it can harm falsifiability (e.g. due to having more tunable parameters).
It's also partly because the models you've seen are motivated by something other than the dark matter problem. Often, we don't dream up models purely to explain away a surprise; we find that a single thing makes sense of multiple concerns. In this case, we have other motives for supersymmetry with $R$-parity conservation, but the lightest supersymmetric partner (LSP) is a natural dark matter candidate.
