I started out training horses in the mountains of Colorado. I rode a LOT of Hancocks. About half of them were going to buck no matter what you did in starting them. The one you describe is typical of the ones that are just cold backed and bronchy by nature. The ones I got were mostly Roan Hancock and Red Man breeding. I started a lot of colts by a horse near me named Roan Light. He was a TAAA race horse and sired a lot of race winners in the 60s. I cannot think of a single colt of his that did NOT buck or try to buck, many times on the 3rd or 4th ride. I learned very quickly not to relax on one of them.
On the flip side (and why the cowboys liked them), they were good footed (could take the rocks) and tough. You could not wear one out. They had really good bone and feet, good withers, were deep in the heartgirth, and di I say they were tough?
I was convinced that the Hancock horses was why so many top saddle bronc riders in the RCA (forerunner of the PRCA) came from Colorado. Wyoming and Montana.
But, like I said, half of them were not bronchy. I just sold my Driftwood bred stallion to a QH breeder in the UK. He was Driftwood and Hancock breeding and you just about can't make one of his colts buck. They are just 'born broke'. Had they not been this way, we would have sold him and all of his get like we have other stallions that we tried.
All the toughness and good bone aside, the Hancocks are often high-hocked and lack the athleticism we have gotten spoiled by in the horses with more 'modern' breeding. Many have a big 'plain' heads and some are downright ugly-headed. Even when they try, they do not flex their hocks when they stop and they are pretty rigid and not naturally very flexible.
This is over-generalizing, but there are so many of them that fit this stereotype, that it is kind of what a lot of trainers think of them in general. In more recent years, breeders that like the Hancocks have done a better job of selecting breeding stock that is better balanced and have nicer heads and attitudes. Hopefully, they keep the toughnes and soundness, but some I have seen did not, but they were sure a whole lot prettier.