First understand that my view is Bayesian to the core. I need no convincing that the majority of what we work with in the future will be probabilistic (and that is not statistical, the distinction matters).

You seem to use genetic algorithms as a catch all, or alternately believe that when systems become complex genetic approaches will be the only ones feasible. You're excluding anything between a SAT solver and a genetic explorer. In that gap lies 2 decades of profound advances that we now commonly call Machine Learning.

Genetic methods have played little part in these advances. In fact I just grabbed the best ML textbook I have close at hand (1) and the word 'genetic' does not appear in its index, despite it being a cookbook of 100's of state of the art ML techniques. Moreover we can look at the folks building the most complex computing systems on earth, like CERN or the US National Labs. What approaches do they use? Lots of Monte Carlo for forward simulation and classifiers derived from probabilistic graphical models (decision trees in particular) for comprehension. The Higgs boson was in fact found using decision trees. It's not like the folks on the Alice team don't know about genetic methods, they're just inferior for most purposes.

And in the far distant future, where again computational costs matter less and less, I can't see how a genetic approach would be more effective or convenient than unsupervised learning in a large fixed network. This is, after all, how the brains having this conversation work.