  It is well known that General Relativity cannot be considered under the
standard of a perturbatively renormalizable quantum field theory, but
asymptotic safety is taken into account as a possibility for the formulation of
gravity as a non-perturbative renormalizable theory. Recently, the entropy
argument has however stepped into the discussion claiming for a "no-go" to the
asymptotic safety argument. In this paper, we present simple counter-examples,
considering alternative theories of gravity, to the entropy argument as further
indications, among others, on the possible flows in the assumptions on which
the latter is based on. We consider different theories, namely curvature based
extensions of General Relativity as $f(R)$, $f(\mathcal{G})$, extensions of
Teleparallel Gravity as $f(T)$, and Horava-Lifshitz gravity, working out the
explicit spherically symmetric solutions in order to make a comparison between
power counting and the entropy argument. Even in these cases, inconsistencies
are found.
