I'm not being very clear with my points. 1) BOSU balls have a place in balance work. But you can get just as much benefit if not more from lifting programs like ones done by mtbsc. Not that you've suggested it but many people think that doing push presses for example on a bosu ball will help their balance. However, if you did them on the ground you'll be able to lift more weight and you will recruit more muscles which leads to better balance and strength. 2) When you are doing deadlifts or squats you actually do not want squishness. Being barefoot or wearing shoes like chucks or nike frees means you are getting more force because (you are not loosing it into the shoe) into the ground and there for lifting more weight and getting stronger. On the other side though. Doing some single leg work like Bulgarian split squats is better served with having your shoes on. If you are playing basketball you want squishy, but basketball players have a high percentage of ankle injuries because their shoes are limiting in the range of motion so when they roll onto them they are more likely to be injured because they don't have a lot of strength through a larger range of motion. So it makes sense to get them out of their basketball shoes and working on their range of motion when they aren't playing. I agree hypermobility is probably a bad thing. But for most people (specially those with seditary day jobs) are so far from being hyper mobile that any sort of ankle mobility work will be beneficial. Especially for mt bikers. If you ride flats how many times has your foot not been quite on the pedals and you hit something that extends your range of motion. There are also linkages to improved ankle mobility and positive effects on low back issues. I think one thing we can agree on is that you should have a plan when you are in the gym. So many people waste their time in there. Just hoping on a bosu ball or kicking your shoes off won't help.

I don't understand you think having less mobility will decrease your risk of injury. A lot of shoes, basketball shoes for example are limiting in their range of motion.

I do agree you can include a BOSU ball in some balance work and but I wouldn't even really suggest using any weights on one. There have been studies that have shown you get more improvements on balance lifting on stable surfaces. "Power comes from the # of reps and explosiveness, not from whether or not you have shoes on." True but if you lift in bear feet or something like chucks you'll generate more muscle recruitment then using even running shoes that have a lot of shock absorbing soles. "Also, working out in bare feet to prevent ankle injury is unnecesary." I never said that. It will increase your ankle mobility though which will improve your lifting.

improve recovery times between training sessions, more power when they pedal, not that it matters for downhill racing but better climbing, better bike control in the air. DH bikes are not light so being able to handle them better physically can only help you.