I know this thread is old, but I think I have some valuable input on the subject. I happen to work for a large rodeo company and a pick up mans family on the West coast, when I can. Yes, a lot of these guys are hired by the stock contracts and the rodeo (you have to appease both parties). Many come from ranching backgrounds, and a great majority of them have actually been bronc riders. You don't pick up bull riders. Getting the cowboy off safely is a goal, but it is not the only goal. A pick-up mans job is all encompasing. He has to look out of the safety of the stock, the cowboys, the officials, the working people in the arena, photographers, etc. A lot of times, he also helps run production, moves stock, treats, medicates, etc. They work in the pens during the day sorting and moving. They work the perf in the evening, and then at night they load and sort what they can. The horses are one of a kind. Just because your horse can rope or doesn't mind dangling stuff and riding bareback, does not mean it will work as a pick up horse. My horse is a failed pick up horse, despite grown up on a ranch, doing brandings, and being a decent head horse. It takes a skilled horse that can handle the pressure in the arena, the job, the cowboy, and more. It's hard. These guys travel a lot during the year and don't earn much money. They are PRCA cowboys without the recognition, big paychecks, or the glory.
Here is a great video on what it takes to the a pick-up man, the horses, and more. https://www.youtube.com/watch?v=AwqgBSxHNrU