#1. Rabbits breed like rabbits. They are in zero danger of going extinct.
#2. Rabbits are pretty tasty. Good for making stew, hamburgers and the meat can be frozen, smoked, and saved for later.
#4. Getting a H2 bowhunting/falconry license is easier than getting a H1 rifle/bowhunting license because you can skip the PAL. Once you have your license small game like rabbits is more readily available then larger game animals like deer and moose, and not limited to such a short hunting season. Plus you don't need to purchase tags like you do for large game.
#5. While rabbits are small and challenging targets, that is actually part of the fun. Any decently skilled traditional bowhunter will be able to nail a rabbit at 20 yards or less pretty consistently.
A good way to practice rabbit hunting... set up a moving mobile archery target like the one in the video below. Rabbits don't like to sit still.