We finally have some answers.
Will Gornall and Ilya Strebulaev have posted a new paper, and their results suggest that the US VC industry is causally responsible for the rise of one-fifth of the current largest 300 US public companies and that three-quarters of the largest US VC-backed companies would not have existed or achieved their current scale without an active VC industry.
We attach a figure from the paper that shows the difference in the number of top public companies founded in each decade in the US and other G7 countries since 1900. The difference since the 1970s when the US VC industry became active can clearly be seen.