Although he does not provide good reasons why teaching statistics as a way into mathematics would be superior to the old way (somebody must have done research on this, right?), it makes intuitive sense to me. He also does not provide a outline on how to strengthen our innate abilities to think in terms of probabilities that would avoid the way stats is often taught at the university and seems to bludgeon any interest in statistics.
The following presentation provides a more reasoned and balanced view on restructuring the mathematics curriculum:
If I can combine both suggestions (as the big compromiser that I am), probabilities/stats sound like a good way to start exploring the diversity in math topics, but that suggestion is also self-serving, because I need students that are comfortable with stats more than with math (although these two things are related).