  We comment on the recent paper by Ghosh and \v{Z}nidari\v{c} (Phys. Rev. B
105, 144203 (2022)) which studies the growth of the number entropy $S_N$ in the
Heisenberg model with random magnetic fields after a quantum quench. The
authors present arguments for an intermediate power-law growth in time $t$ and
a sub-ergodic saturation value, claiming consistency of their results with
many-body localization (MBL) for strong disorder. We show that these
interpretations are inconsistent with other recent studies and discuss specific
issues with the analysis of the numerical data. We point out, in particular,
that (i) the saturation values $\widetilde{S}_N(L,W)$ for fixed length $L$ are
only bounded from above by 'the ergodic value' and are already far below this
value for $W\ll 1$. Furthermore, the saturation values can show non-monotonic
scaling with $L$. (ii) Power-law fits $S_N(t)\sim 1/t^\alpha$ -- with
$\alpha=1$ expected based on the resonance model described in the paper --
yield a system-size dependent exponent $\alpha$ while fits $S_N\sim
\frac{1}{W^3}\ln\ln t$ do hold independent of system size and over several
orders of magnitude in time. (iii) We also argue that for the cases where the
effective resonance model works best and predicts a saturation of the number
entropy, the same applies to the von-Neumann entropy, i.e.~the dynamics at the
considered scales is of single particle type and unrelated to MBL.
