Q.Why golden barrel cacti propagate pups
We have a number of 12-15 year old golden barrel cacti in our yard. Recently, some have begun to spawn pups and others have not. Is there a reason why some do and others don’t?

The Barrel Cactus is growing little Cactus pups and it is part of the natural growth pattern for this plant.
You can remove them and grow new plants.
Here is a few articles that have more information.
https://www.gardeningknowhow.com/ornamental/cacti-succulents/scgen/removing-cactus-pups.htm
https://www.gardeningknowhow.com/ornamental/cacti-succulents/barrel-cactus/barrel-cactus-care.htm