  The superallowed Gamow-Teller transition in the doubly-magic-shell nucleus
$^{100}$Sn and the high resolution spectral shape analysis in the
fourth-forbidden nonunique transition in $^{115}$In indicate as much as $\sim
40\%$ {\it fundamental} quenching in the axial-current coupling constant $g_A$
in nuclei. This can be attributed to an effect of the trace anomaly in QCD
"emerging" in nuclear medium. If confirmed, this would signal a major revamping
to do in nuclear interactions consistent with chiral-scale symmetry in nuclear
medium and a big impact on $0\nu$ and $\nu\nu$ double $\beta$ decays for BSM. I
present an argument that such a big anomaly-induced quenching is incompatible
with how hidden scale symmetry manifests in nuclear medium, A possible means to
resolve this issue is discussed in terms of hidden scale symmetry permeating in
baryonic matter from normal nuclear matter to massive compact-star matter.
