The best situation for genetic diversity is to take out a buck soon after he has passed on his genes.
True -
But a heathly herd is not about genetic diversity - its more centered around buck:doe ratios and age structure.
If we were looking at changing the makeup of a particular herd - you would be correct about about the quickest way to encourage change. But -by taking deer right after they breed - There is no dominance established - and the local herd remains in a state of flux until a few deer live through a season or two.