  We use the \texttt{GRUMPY} galaxy formation model based on a suite of
zoom-in, high-resolution, dissipationless $\Lambda$ Cold Dark Matter
($\Lambda$CDM) simulations of the Milky Way (MW) sized haloes to examine total
matter density within the half-mass radius of stellar distribution, $\rho_{\rm
tot}(<r_{1/2})$, of satellite dwarf galaxies around the MW hosts and their mass
assembly histories. We compare model results to $\rho_{\rm tot}(<r_{1/2})$
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 $\rho_{\rm tot}(<r_{1/2})$ 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
$\Lambda$CDM-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 $\Lambda$CDM 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.
