If the population of the herd overgrows the food source the deer will die anyway. Hunting is highly regulated. You can't just go out and shoot anything you want whenever you want. You have to get licenses and there are limits in locations and by animals or fish. If you want to hunt a deer, you have to pay to get in a lottery. They draw the number of tags based on the number of animals in the population. Also, there are limits on the sex of the animal that you can shoot - they don't want to kill off all the does, for example. In Idaho, they are begging hunters to shoot wolves because they are killing off other animal populations (there are too many). When the population gets down to a mangeable level, they will restrict the hunting again. There are also lakes where fish were introduced illegally that they use fisherman to get rid of the unnatural fish population.
The money used to purchase guns and licenses supports the environment. All these items have taxes on them used for sustaining and supporting the animal population and the environment where they live.
As for there being too many deer...we have herds of them, yes HERDS running through our yards and neighboorhoods. There is no shortage of deer, at least not here.