I’ve done well on lottery tags over the years. I’ve drawn once in a lifetime Oryx in WhiteSands, Persian ibex in the Floridas, and Vermejo Park Elk in NM. I’ve drawn Mt Goat, and bull Moose in Colorado. The only lottery draw I’ve never hit anywhere is Big Horn sheep. I might never draw one but if you don’t try you’ll most definitely not draw one.
It doesn’t cost much to put in and if you do draw the cost is multitudes less than buying a land owner tag and mega bucks less than doing a guided hunt. Obviously on the species that have limited draw tags if they were to be over the counter there’d be non left in short order. There is a very good reason why lottery tags are limited and huge conservation tool.