"Basic economics tells us that wages do not rise because of unions, but rather because people have become more productive..."

On the contrary, our history tells a different tale.  Incomes increased steadily through the post war era through the 60s into the 70s along with productivity.  This was also the time of the greatest density of Unionized workforce.  As the attacks on Unionization increased and were more successful in decreasing Union density wages stagnated and even fell (after adjusted for inflation) even though productivity increased.