I’ve always heard that gold prospectors used them because they could survive on most any kind of vegetation, whereas horses required much more food and water.
Makes sense. Grandfather also makes the point in the article that their backbone is wider, allowing them to carry more. One of the articles describes him being bitten by a sidewinder, strapping himself to a burro and going unconscious as the burro carried him to safety, the rest of the string following, as trained.