Firstly, culling 2000 elephants a year wouldn't change the population much, and the goal of culling is to reduce the population. What @Sackrider describe is harvesting, nothing more, nothing less. Harvesting 2000 elephants a year can be done though, and there are enough people willing to pay for that, unlike @ZaminOz thinks there are thousands, probably over ten thousand, of American hunters going to Africa each year to hunt. A few thousand will go to Zimbabwe and hunderds of them used to shoot elephants. Not just trophy bull elephants, but what's actually a popular hunt is shooting tuskless female elephants. If they would sell it as a cull hunt, it would typically carry lower day rates and much lower 'trophy' fees, but each hunter would should more than one elephant. This would reduce the revenue quite a bit though. And if it's truly culling, whole herds should be shot, to have as little impact as possible on other herds. I doubt hunters will have a problem with shooting calves as long as it's in line with their thoughts of what is good conservation.
On the meat front though, it would be very difficult to collect and distribute the meat to communities in time. One elephant is usually easily dispatched, often done by villagers themselves. But if you cull inside the park, far away from villages, you don't have those extra hands at hand. Culling a family herd of 6-10 elephants, then cutting them up, loading them into trucks, drive the trucks to villages hours away to distribute the meat you would need a sizeable crew of people to do this, plus several off-road refrigerated trucks. And the beef industry in the country might not be happy with it and cause trouble to raising questions about health issues as the meat is not checked, the animals are not checked etc.
And like @Geoff said, it will also have an impact on photographic tourism.
@Soukous Hope you find that report, looking forward to it!