  The idea that the gravity-induced breaking of global symmetries is encoded in
Planck-suppressed operators is not scale-invariant: heavy particles which have
nothing to do with the UV completion of gravity can mediate the breaking and
produce low-energy operators (partly) suppressed by their own mass scales. Such
contributions from heavy fields are typically subdominant with respect to the
least Planck-suppressed operators, unless the latter are forbidden, as is usual
in solutions to the axion quality problem based on four-dimensional gauge
symmetries. Therefore, with a focus on axion physics, I investigate such
situations and present toy examples where a non-minimal sector of heavy fields
coupling to the axion generates operators whose coefficients are orders of
magnitude larger than the naive Planck-suppressed estimates, despite gravity
being the only source of breaking. I also stress that the key features of these
toy models, namely several families of heavy fields with family-dependent gauge
charges, are already present in some non-minimal QCD axion models, using the
axiflavon/flaxion and the lighter-than-usual KSVZ axion as examples. This
suggests that gauge-symmetry-based solutions to the axion quality problem, or
of any quality problem really, need to describe complete UV scenarios or make
precise UV assumptions.
