I think, the main effect of sexual reproduction is that, much like GANs and competitive self-play, it creates species-internal competition: Both sexes need to impress, which makes cheating an obvious strategy (makeup, steroids, Shakespeare quotes, LISP etc., but many such examples can be found in the animal world), and hence both sexes also need to be able to detect cheating. Some species are rather asymmetric in that regard. For example, in humans it is mainly women who attract (they masquerade as fruits [make up is likely a cross-cultural phenomenon; and, well, breasts] tapping into male food gathering circuitry); men compete in hierarchies trying to impress and women select men from the top of the hierarchy. Complex dynamics emerging from this likely lead to the immense growth of the human cortex.

Sexual reproduction basically outsources some of the selection effort to the cognitive apparatus of the species itself, thereby introducing a massive amount of additional selection signals (mainly by the much increased necessity to model other minds, namely minds of the opposite sex). Many of these signals promote traits that are useful for survival (mainly intelligence and health).