Some national parks already have lottery systems for certain areas, e.g. to hike to the top of Yosemite's Half Dome: https://www.nps.gov/yose/planyourvisit/hdpermits.htm
Some more: https://www.usatoday.com/story/travel/destinations/2018/04/0...
Some more: https://www.usatoday.com/story/travel/destinations/2018/04/0...