Very thorough and great statistical work, but it's all arguing against a weak premise.
His insight was that 2nd and 10 disproportionately followed an incomplete pass. This generated two hypotheses:
Coaches (like all humans) are bad at generating random sequences, and have a tendency to alternate too much when they’re trying to be genuinely random. Since 2nd and 10 is most likely the result of a 1st down pass, alternating would produce a high percent of 2nd down rushes.
Coaches are suffering from the ‘small sample fallacy’ and ‘recency bias’, overreacting to the result of the previous play. Since 2nd and 10 not only likely follows a pass, but a failed pass, coaches have an impulse to try the alternative without realizing they’re being predictable.
The argument boils down to coaches trying to catch the defense off-guard; they are either alternating to be random or "overreacting".
It may not be that complicated. Coaches hate 3rd and 10 or more specifically third and long. Analysts emphasize it every game and the reason why is because at that point there is no randomness. You pretty much have to pass on 3rd and 10 and the defense knows this, not to mention a play that requires ten yards takes longer to setup than a play which takes four and the defense is already rushing your QB...
If you have an incomplete pass on 1st and 10, you pass again on 2nd and 10 and have another incomplete, you're now looking at passing on 3rd and 10: 3 passes in a row, no time burned off the clock (time of possession is also highly valued), and no momentum - you've just fucked up on the same play two times in a row and you've got to run it (well pass it) again.
You run on second down, you'll usually at worst get a yard or two, but you very well could have a good run and you're then looking at 3rd and 6, third and 4, situations that open up your playbook a lot.
This might not be the reason coaches do it, but it's certainly a possibility. They seem to get into an argument of causality when they've got some interesting correlations. But I just armchair quarterback so don't mind me.