Naturalness in Physics and fundamental constants

From the "flatness problem" in Cosmology to the "strong CP problem" and "hierarchy problem" in the Model standard, a lot of problems in physics deal with Naturalness: a certain parameter in our theory is too small or too big and so we look for a better understanding of it. To resolve this "unnatural fine tuning", in Cosmology Guth proposed the Inflation, and for the Standard model we have the SUSY hypothesis.

If so, why there isn't a naturalness problem also for the velocity of light and all the fundamental constants that we know in nature? It seems to me that the only way to prevent a naturalness problem is to create a theory that determines itself with no free parameter, and this is impossible.

• Comment to the post (v2): Naturalness is linked to that dimensionless physical constants should be "of the order 1". E.g. the speed of light $c$ is not dimensionless. Which dimensionless physical constants are you thinking of? Related: physics.stackexchange.com/q/8373/2451 – Qmechanic Dec 11 '16 at 20:11