  It has been shown, via specific examples and a pseudospectrum analysis, that
the black hole quasinormal spectra are unstable. The implication of such a
result for gravitational-wave physics and of our understanding of black holes
is, still, unclear. The purpose of this work is twofold: (i) we show that some
of the setups leading to instabilities are unphysical and triggered by exotic
matter or extreme spacetimes; (ii) nevertheless, we also show simple examples
of compelling physical scenarios leading to spectral instabilities. Our results
highlight the importance of understanding the overtone content of time-domain
waveforms, and their detectability.
