  In their recent preprint [arXiv:2108.07893v1], S. Panahi, N. Amaya, I.
Klickstein, G. Novello, and F. Sorrentino tested the simultaneous block
diagonalization (SBD) technique on synchronization in random networks and found
the dimensionality reduction to be limited. Based on this observation, they
claimed the SBD technique to be a failure in generic situations. Here, we show
that this is not a failure of the SBD technique. Rather, it is caused by
inappropriate choices of network models. SBD provides a unified framework to
analyze the stability of synchronization patterns that are not encumbered by
symmetry considerations, and it always finds the optimal reduction for any
given synchronization pattern and network structure [SIAM Rev. 62, 817-836
(2020)]. The networks considered by Panahi et al. are poor benchmarks for the
performance of the SBD technique, as these systems are often intrinsically
irreducible, regardless of the method used. Thus, although the results in
Panahi et al. are technically valid, their interpretations are misleading and
akin to claiming a community detection algorithm to be a failure because it
does not find any meaningful communities in Erd\H{o}s-R\'enyi networks.
