Dan Gable is The King
First a pretty graph showing the years that each coach coached and the percentage of the bracket that AAed each year. The % of a bracket to AA takes into account both the bracket size and the number of AA's each season (which was variable over the time period). The assumption is that the higher the % of the bracket to AA, the easier it is to AA. I don't know if this is exactly correct. In the open era with more wrestlers in the bracket there is, I believe, a higher incidence of soup cans. In the qualifying era that gets sorted out before the tournament. So take it with a grain of salt.
Next a table. Based on AA's per season Gable is clearly head and shoulders above the rest, with Cael Sanderson a distant second. But I also wanted to adjust for field size and number of AA slots (in spite of the caveat above) so I also calculate the percentage of all AA's available during their tenure that each coach earned. Again, Gable runs away from the field, but now Harold Nichols pips Sanderson as there were between 4 and 8 AA's per weight and between 8 and 11 weights during Nichols' tenure.