  The unprecedented image of the M87* supermassive black hole has sparked some
controversy over its usefulness as a test of the general relativistic Kerr
metric. The criticism is mainly related to the black hole's quasi-circular
shadow and advocates that its radius depends not only on the black hole's true
spacetime properties but also on the poorly known physics of the illuminating
accretion flow. In this paper we take a sober view of the problem and argue
that our ability to probe gravity with a black hole shadow is only partially
impaired by the matter degrees of freedom and the number of non-Kerr parameters
used in the model. As we show here, a more intriguing situation arises from the
mass scaling of the dimensional coupling constants that typically appear in
non-GR theories of gravity. Existing limits from gravitational wave
observations imply that supermassive systems like the M87* black hole would
suffer a suppression of all non-GR deviation parameters in their metric, making
the spacetime and the produced shadow virtually Kerr. Therefore, a supermassive
black hole shadow is likely to probe only those extensions of General
Relativity which are endowed with dimensionless coupling constants or other
special cases with a screening mechanism for black holes or certain types of
spontaneous scalarisation.
