I propose to ask, what is the meaning of the thesis that the soul is a harmonia, and then to examine Socrates' arguments against Simmias. The word 'harmonia' may have different shades of meaning (I distinguish at least four), and the arguments must vary accordingly.
I conclude that the arguments of the Phaedo are not decisive against any version of the harmonia thesis. Their main importance lies in making explicit the incompatibility of physical determinism with a view of the non-physical soul as an autonomous agent, but this is far from showing that the deterministic thesis is false.
Taylor, Christopher C.W., "The Arguments in the Phaedo Concerning the Thesis that the Soul is a Harmonia" (1970). The Society for Ancient Greek Philosophy Newsletter. 80.