Why would (unsupported) single leg squats, or one arm push-ups or pull-ups (maybe with an additional weight vest or some weight) not work? I feel the math could be made to look equivalent and, just observationally, I don't think a lot of people are ablke to do single anything so there should be plenty room to grow? As far as I am able to tell without having done any, barbells are "simpler" because you can scale them fairly smoothly.

You just aren't moving the same amount of weight with those exercises. If I'm squatting 300 pounds, while most of the time the weight is distributed, there will be moments where one of my legs is balancing close to 300 pounds. There will be no moment anywhere close to that with a single leg pistol or skater squat. Those are great exercises, but you'll get a different outcome IMO.