Over time, this caused morality to be biologically hardwired into the gene pool.

The sheer diversity of moral theories actually applied by some human society at some point in history makes this claim extremely difficult to accept.

It's likely that most moral positions are consistent with decision theory (i.e. Tit-for-Tat wins many iterated Prisoner's dilemma tournaments). But that doesn't require that morality be "baked in" by evolution. The generalized view of organisms as adaption-executors seems sufficient to explain why basic decision theory bears some resemblance to the relatively uncontroversial moral positions.