Off the original topic, but odds would improve much more if everyone were limited to choosing 1 of either deer, elk, antelope, sheep, moose, or mtn goat. Keep the general deer and elk tags if you want, but pulling people out of 5/6 draws will improve the odds far more than making harvest once in a lifetime.
More on topic, the OTC hunts are a huge source of sheep advocates and advocacy, giving regular folks an opportunity to get into sheep hunting. Making sheep harvest once in a lifetime doesn't decrease harvest or increase anyone else's opportunity. Hpwever, I think if you shoot a ram under 5 years old on an OTC sheep tag, you should have that be your only ram in any state, ever.