Here is the point you are missing. Fairness amongst shared owners and the effect of hunting on the limited animal population doesn't change between scenarios of 1,000 applicants for 500 tags vs 10,000 applicants for 500 tags. The biology of the limited resource is the SAME. And if done randomly, the resulting fairness/equity for all the shared owners is the same.
What is different is that if one of the original 1,000 could somehow block the extra 9,000 hunters from applying - then their personal odds would be much better while having ZERO effect on animal populations. And how could we achieve this? Well, what if we give the vested initial hunters extra chances in the draw that keep them ahead in the drawing process for much of a lifetime, or maybe let hunters have their parents buy them preferential draw status when they are still in diapers, or maybe half our population (women) shouldn't be encouraged to hunt, or maybe the 80% of the population who don't live within easy access of hunting should be discouraged from even trying, or what if folks from other places have to pay more, or what if nobody knew how to do it unless their father taught them because we over-tax and regulate 1A protected speech of public hunting advocates who use modern media, or we give outfitters and landowners transferable tags to "sell" to their long time clients, or what if minorities were not welcome, or, or, or . . .
So, the premise of "hunting media is bad for animal populations" is just a ruse for one owner trying to cut a fellow co-owner out of an equal chance to share the enjoyment of their shared resource. But then again, so many other parts of the western big game hunting game are being done for the same reason.