@rocrat thanks for raising this topic and giving us the opportunity provide a few details about REI trips!
In Southern AZ, where you mention your family likes to backpack, there is one backpacking destination where we host small groups that limits the number of permitted hikers/backpackers at 50 people per day. For this destination, BLM issues all permits and REI acquires our permits by the same process and timeline as an individual who wishes to explore in the region. Our groups include up to 10 people, including a guide, so on the days we host trips, we represent less than 20 percent of all entrants.
For the remainder of 2021, we have nine departures scheduled, equating to fewer than 100 people for the year and equating to less than two days in total as BLM issues 50 permits per day. In addition, at no time do we have more than one group in the region.
We hope you find this information helpful!