The $\Lambda\rm CDM$ (cold dark matter with cosmological constant) is the current standard model of cosmology because the model comes with a long list of phenomena successfully explained by it. However, there are a remaining handful of problems which are not yet resolved in the context of $\Lambda\rm CDM$, for instance (with links to my picks for reasonably accessible and/or up to date technical papers):
- The too big to fail problem
- The cusp-core problem
- The missing satellites problem
- The disk of satellites problem
These (perceived? it is as yet unclear whether these issues can be resolved within the $\Lambda\rm CDM$ framework) problems have prompted many research groups to look at alternate theories. Some examine modifications or alternatives to general relativity - since much of the evidence for the existence of dark matter assumes GR, an alternate theory of gravity might make DM obsolete. For the purposes of this question, I want to retain the assumption that GR is correct. The other approach is to question the cold part of CDM. There is evidence ruling out hot (i.e. relativistic) dark matter, but so called "warm" dark matter (WDM) is an area of active research. There's also been some buzz about self-interacting dark matter (SIDM, i.e. interaction couplings within the dark sector). There are a number of papers claiming solutions to the $\Lambda\rm CDM$ problems in the framework of WDM or SIDM, or rather more conservatively the magnitude of the problems can be at least alleviated with alternate dark matter models.
However, I assume that the scientific community hasn't fully embraced WDM because it has trouble in other areas where CDM is just fine. What is/are the observations that WDM/SIDM/other-alternate-DM have trouble explaining that prevent them from replacing CDM as the standard model of cosmology? Or is one of these alternate models now competitive with CDM and we just need compelling evidence that WDM solves the remaining problems in CDM before re-writing the textbooks, so to speak?