Are all models of self-interacting dark matter proposed just to solve this problem of dark matter-baryon distribution you mentioned above? If it's not only that.. then what other observed distributions needs the self-interacting dark matter model.. And why is there a second baryonic-DM interaction model. Can't we decide based on the observations whether it is best modeled using purely self-interacting DM or baryonic-DM interaction?Not true. The evidence is that completely collisionless DM is inconsistent with the observed distribution of DM. Therefore, there has to be either self-interaction in DM or a baryonic-DM interaction or modified gravity. See, e.g.:
* Paolo Salucci and Nicola Turini, "Evidences for Collisional Dark Matter In Galaxies?" (July 4, 2017). Abstract:
* Dark matter distributions have to closely track baryon distributions, even though there is no viable mechanism to do so: Edo van Uitert, et al., "Halo ellipticity of GAMA galaxy groups from KiDS weak lensing" (October 13, 2016).
Absolute no paper that explores the fifth force whether it is based on gauge field, abelian/non-abelian and viable/plausible symmetry breaking mechanism and whether it is connected at all to the electroweak mechanism?