Doubt a mule would get a bruise on its sole very easy. I've ridden mules in about every condition there is, and never had a bruise or abcess. Had several horses get sore in terrain that wasn't all that challenging. Boots don't stay on, and cause stumbles. Technology might have led to a better boot. Idk the only time I use them is tieing a horse to the trailer overnight on gravel, or if I'm stalling on concrete. Also, unless they make a boot for a mule, a horse boot is probably not going to fit. Not much flare to a mules foot.
New product out now, you pour on the sole of a thin soled horse. Works like an epoxy, but stays reasonably soft. You use it when your going to be on jagged rocks, and take it out when your done. Supposed to be good stuff, but I've never used it.