I don't necessarily buy the "people have to have a chance to hunt sheep to care about them" narrative, there could hardly be a worse ROI on anything you put your time to, you either care about sheep on the landscape because sheep are cool, or you couldn't care less, and your 1% chance of ever drawing a sheep tag probably doesn't change that in a meaningful way, I feel like the couple hundred people who draw a sheep tag each year are the ones who after the experience are the biggest sheep advocates, and it doesn't have to do with getting another chance? seems like the more individuals you can get into the mountains chasing sheep the more advocates you create, while the more people who get bitter by watching someone else draw their 3rd sheep tag don't want anything to do with sheep? I could be wrong about the majority of people though, I think it's really hard to guess how this would actually play out.
The community service requirement would be a great idea, plenty of ultra runs with horrible lottery odds have a mandatory trailwork requirement to either get into the lottery or improve your odds... I see zero chance of that actually happening but the idea has been wildly successful elsewhere.