What happens if we instead consider a pair of charged bodies with different charges and replace the constant gravitational field with a constant electric field in the vertical direction? Suppose that both charged bodies are attracted by the ground and that no gravitational field is present.
In Galileo's reasoning no description of the gravitational interaction is actually provided, so gravitational field could be replaced by the electric one.
Along Galileo's reasoning should we conclude that the charged bodies will reach the ground simultaneously? It seems so.
It would be generally false, obviously, also because what happens also depends on the inertial masses of the bodies, that play a role but are not mentioned. So, in my opinion Galileo's reasoning is untenable.