I'm not familiar with the ins and outs of all these systems, I can't afford and auction tag short of winning the Powerball. I don't keep up on them.
If a tag, or anything else, is sold at public auction, then I fail to see how it is not a public item. The final cost and who and how it was created are not relevant to the fact that anyone is allowed to bid on the item. I see that as pretty black and white. If there were a set number of people/names on a list and they were the only people allowed to bid, then I would agree, not a public tag.
As far as changing laws, seasons etc. That is already done and happens with other tags and hunts. There are special youth seasons, within those seasons youth are allowed to take game that would otherwise be antler restricted. There are special handicap regulations, allowing those to use means to take game that are not allowed by others. The Game and Fish doesn't operate under a blanket set of rules and restrictions. They change things for what would hopefully be the betterment of the sport.