I don't believe that the rise of the left and lowered IQ's are incidental to each other.
There is also a growing IQ gap. Highly intelligent people tend to have children with other highly intelligent people. Less intelligent people tend to do the same. The welfare state has subsidized several generations people who are generally less intelligent than average. Do a YouTub search for Stefan Molyneux and listen to some of his lectures on IQ and how it impacts society. A lot of it is pretty terrifying but there is ample evidence to back it up