Even that was not the decisive problem - given enough compute multilayer NNs could be trained just fine. The real obstruction was a political failure of deep learners (connectionists) in securing academic prestige and associated access to large-scale compute; By now it's all but forgotten, but then this was a prominent academical political debate of the decade: https://en.wikipedia.org/wiki/Neats_and_scruffies and even though "neats" eventually prevailed, the connectionists were still sidelined by statistical ML practicioners (whose efforts didn't happen to scale, although more than a few weighty theses and books happened to be published as a result).
Perhaps in the near future, when this wave of AI will give us impossible to deny life-changing outcomes (for example: new cures for chronic diseases) we will look back and think about how many years or even decades of progress were postponed, essentially lost for nothing but academic hubris of a camp that won the funding battle then, only to be swept away in a few decades.
Until we haven't really understood the Bitter Lesson http://incompleteideas.net/IncIdeas/BitterLesson.html every bit of progress that was not realized is our fault.