We use the GRUMPY galaxy formation model based on a suite of zoom-in, high-resolution, dissipationless Λ Cold Dark Matter (ΛCDM) simulations of the Milky Way (MW) sized haloes to examine total matter density within the half-mass radius of stellar distribution, ρtot(< r1/2), of satellite dwarf galaxies around the MW hosts and their mass assembly histories. We compare model results to ρtot(< r1/2) estimates for observed dwarf satellites of the Milky Way spanning their entire luminosity range. We show that observed MW dwarf satellites exhibit a trend of decreasing total matter density within a half-mass radius, ρtot(< r1/2), with increasing stellar mass. This trend is in general agreement with the trend predicted by the model. None of the observed satellites are overly dense compared to the results of our ΛCDM-based model. We also show that although the halo mass of many satellite galaxies is comparable to the halo mass of the MW progenitor at z ≳ 10, at these early epochs halos that survive as satellites to z = 0 are located many virial radii away from the MW progenitors and thus do not have a chance to merge with it. Our results show that neither the densities estimated in observed Milky Way satellites nor their mass assembly histories pose a challenge to the ΛCDM model. In fact, the broad agreement between density trends with the stellar mass of the observed and model galaxies can be considered as yet another success of the model.