I think horses like that are good teachers. It's a balance, though. Some green horses can just be nutcases under saddle that quickly get out of control if you don't get it. I know some broke horses like that too, though. The trainer trusts me to ride them because if the situation did get out of hand I would be able to handle it without getting angry or scared into doing nothing. I might not have he best seat or balance but I for some reason have a knack for dealing with green horses. It gets them used to a less balanced seat without putting someone who doesn't know what to do on them.
I'm guessing my ability with that comes from the years of riding I had beforehand. I "know" how to deal with those situations it's just a matter of muscle memory. Most riders who look the same as me in the saddle would not have any idea what to do if a horse started bucking (and I've sat quite a few of those over the last for months ).
That being sad, I'm a little annoyed that none of the trainers I work with (2 different barns) will put me on a lunge line. They don't think I need it but I just know if I got on a line for a few days I'd fix the issues I had at the posting trot.