Well, yes shotguns are legal in several western states. I looked at Colorado which simply requires a 20 gauge or bigger firing a single slug (not buckshot). New Mexico requires 28 gauge or bigger with a single slug. I don't think Oregon even worries about gauge.
As to effectiveness, muzzleloader seasons are very popular for elk here in the US. Usually the requirement for elk is 45 or 50 caliber minimum. As a practical matter, most use a 50 caliber with a very few using something with a larger bore. I mention this as modern sabot slug loads are generally comparable to stout muzzleloader loads in range and power. A lot of elk get killed during the muzzleloader seasons. Not many hunters will use a shotgun for elk during the rifle season.
Grandpa's old 12 gauge firing a brenneke load is plenty lethal at short range. I don't think we worry too much about someone using "too little" when it comes to shotguns. I have seen hunters using a 20 gauge once in a blue moon but just almost everyone deerhunting with a shotgun is using a 12 gauge with 2 3/4 or 3 inch slug loads. Big slugs at close range and placed right are sure killers.
As shotguns vary a great deal, you may want to focus on requiring rifle type sights and not less than 20 gauge. If the shotgun has open adjustable iron sights or an optical sight mounted, then you have some reason to believe the shotgun has been set up properly and perhaps even sighted in. Rifled barrel shotguns are plenty capable at extended ranges with the right ammunition. Smoothbores can do better than you might expect but are a shorter range proposition.
I will say that I think worrying about sights is probably working too hard to solve a problem you're unlikely to have. If your hunter is using a smoothbore, has fired it before to check point of impact (made sure that his gun doesn't throw slugs wild or high) and limits his range to around 25 yards (depending on her gun and load combo), he or she will be eating venison.
