That's what all dominant males in herd animals do. The principle has worked for millennia. Incest is a wholly human concept. I have not seen any suggestion that the shooting was necessary to maintain the gene pool.

If the shooting was for genuine stock/herd management purposes and had taken place outside the rut it would be unobjectionable - compare the US culls of bison. But neither of those tests, apparently, were satisfied.

By way of comparison, there is an almost complete ban on taking freshwater coarse fish from English waters, because, allegedly, of the need to maintain stocks.