The major ... problem can be that these farms are in heavily populated areas where the deer come out of housing, parks and areas inaccessible to hunting, hammer the famer's fields, then go back to the sanctuaries. A deer consumes 7-8lbs of vegetation a day. Take my guy's 23 deer, that's over half ton of crop per week, almost 3 TONS in a month! Or, picture 3 tons of prize petunias being eaten in wealthy neighborhoods where those rich people have political clout...lol To hunters, they see every deer as a potential 18pt wall hanger buck that will have them a legend & bragged about for decades. To a farmer they see deer as 180lb rats taking food off their tables and stealing their mortage payments.
As for herds "bouncing back," an unchecked deer herd, given the habitat & nutrition, will increase in size 40% a year!!! A farmer with 20 deer eating this crops this year doubles to 40 deer two years later, and in just 3 seasons is up to almost 60 deer. Some of the most surprised, and taken back looks I've gotten during meetings with communities and landowners who have gone through hell to get to the point of actually killing the deer wrecking their property, is when I tell them "deer management is FOREVER." You can't drop a herd down to carrying capacity of the habitat, then think you're done. It's all over. The problem went away. 40% per year adds up fast. I've seen more than a few places where they quit after three years of a professional solution got the deer under control. The community stopped the cost. Only to be overrun again with deer and looking for help 4 years later.
My last "fun fact" is hunters claiming "all the deer are dead." Biologists consider 15 to 20 deer/mile the maximum carrying capacity for good habitat. Just for reference they think that the land was carrying about 9 deer per mile when the Pilgrams landed here in 1620. When you have 25-30 deer per mile hunters don't see deer. It takes experienced hunters willing to kill does approximately 38-40 hours in the woods to kill one deer at 30/mile. They might not see a single deer in a day. Hunters want 50-60 deer per mile to have an enjoyable hunting experience... to see enough deer to keep them happy. You can see the major clash or conundrum in the situation. Biologists, farmers, landowners, insurance companies want 15. Hunters want 60+!!! That's one reason that even successful deer management programs eventually fail. If you CAN manage to reduce the herd using firearms, archery and even professional sharp shooters, the problem is "maintaining" the herd at those low densities. Keeping fannies in the trees when the boomer bucks are dead and you have to sit 38 hours to kill one deer. The participants quit and go hunt at Uncle Joe's cabin they see deer and might kill a decent buck.