One of my evolutionary computation professors said that he had a deck of cards that he carried from job to job, university to university, running bits of his evolutionary computation experiment on spare cycles, an experiment that runs in fractions of a second on hardware at the time he told the story in 2001. Presumably now it would run in even more fractional fractions of a second.
It's become increasingly clear that Chomsky's approach to language is not going to generalize to AI successes or explanations of many domains of human performance, as was promised. That approach has not yielded fruitfully anywhere except the narrow realm of syntax (in particular typologies of syntax). While machine learning has kicked butt left and right.
There is no reason people can't go on studying syntax at the same time machine learning expands. But it would be dishonest to ignore the extreme and exclusive claims laid down by Chomsky's school at the outset of the cognitive revolution. These claims were given a very liberal benefit of the doubt for decades. A lot of good work has been done in syntax. But now those claims about AI and psychology-in-general are clearly threadbare, since they have not yielded the promised fruits either in AI or in explaining human functions. They have not even yielded plausible IOUs. Remember, this was supposed to explain pretty much everything. Not even language acquisition has been explained.
That is empirical inadequacy. Who cares if Chomsky thinks it's beautiful?
And it's equally clear that learning of various kinds has to occur and also gives us the more parsimonious and elegant solutions to problems (no-solution and no-explanation is not elegant even if it is simpler).
Machine learning has a great deal of conceptual beauty - if you study it rather than pooh-poohing it because of some facile abductive argument to UG.
Computing power isn't a problem. The scale of the human brain is enormous and we are still nowhere near reaching it with our computational resources.
In particular, statistical approaches have been used for a long time, but were not practical until fairly recently; it was the lack of "big data" computing power holding them back more than anything. Statistical machine translation and parsing experiments have been tried on and off for decades, but with 1950s-era data they produced total garbage as output, even worse than the (also bad) symbolic approaches. Hence why Shannon's work on text processing didn't produce practical NLP or NLG systems. It took Google-sized data to produce statistical translation that was actually usable.
What numerical approaches were possible on computers of the time were fairly extensively investigated when they became possible (e.g. the 1980s focus on "sub-symbolic AI", with perceptrons, neural networks, numerical regression methods, etc.). Some were shelved for years because they just didn't work as well, e.g. symbolic game-tree search massively outperformed machine learning in board games in the early experiments, which is why Samuels's 1950s ML-based checkers player was theoretically intriguing but not considered very practical.