I posted an analysis
of how competitive the matches were at the USTA Clay Courts. The basic point is that you only need to reduce the draw until (A) most first round matches are competitive, or (B) most seeds have a competitive opening match. You also want to avoid excluding players who proved they belonged, as I also mentioned
The same logic applies to all levels of tournaments, from Champs and Challengers (a.k.a. top two levels of sectionals) up to L3 and L2 nationals and then L1 Supernationals.
If the USTA had done such an analysis, they would have already posted the numbers. Obviously they did no such analysis, but they might have gotten a few things right by accident, I suppose.
I also doubt that each age group of nationals would end up with the exact same recommended draw size after such an analysis. The proper sizing to make a funnel shape that suits the numbers and quality of players depends on such an analysis.
EDIT: It is also possible that boys and girls do not need the same draw sizes to create the right funnel shape.