If a kid wants to hunt, he or she will find a way. Out of state big game hunts are not the only option. You don't do your kids any favors by bargaining with them to "recruit them". I remember vividly the first time I was allowed to accompany the grown men hunting. Right down to the snacks we ate up on the mountain. I was 12. That was 55 years ago. I didn't actually get a license and hunt for two more years. I still chased rabbits with an old recurve in the fields on the edge of town until then. I didn't get to hunt out of state and for elk until I was in my 30's. My son killed his first deer at 13. A couple years later, he told me he just didn't want to any more so I went alone or with friends. Now he wants to hunt with me and we have the last few years. Way back when he was 12, I bought him a UT deer tag and license. Full price. He ate tag soup. I also paid for his ID tags and licenses (NR). He wanted to but I paid it because I wanted to. He is 43 and has a family to provide for.
I hope your son keeps hunting but if it is just for the out of state elk hunts, then maybe he's really not into it yet.