This is arguable, I think it depends on the horse and the way they are bred.
I have one Hancock who absolutely could never, and another that looks like a warmblood and has made a great H/J & dressage horse (western & english).
If Hancock himself isn’t in the first 2 generations of a horses pedigree, his genetics are pretty diluted by the rest of the horses in the pedigree. Essentially, you cannot affix a horses temperament to only 1 horse in the horse’s pedigree. There are too many other contributors to every horses attributes.
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I started riding at 32 yo.
My first Hancock horse was heavily Hancock bred. A bay roan. Solid trail horse tough as nails and lived to eat up a cow penning.
My second Hancock horse was out of a Blue valentine grandson. Smart. He was lighter boned. Trainer said he was the easiest horse he’d ever broke.
My third horse was a foal out of a Leo Hancock Hays son and was a nice one that I regret selling to this day. Smart.
I’ve ridden a mare that was newly broke that was a Hancock horse and she was personality plus and took to trail riding after being newly broke. Unflappable. Big tall heavy wench!
I’ve also ridden a Driftwood /Hancock gelding shortly after he was broke and he was quiet and solid. He was a blast to ride.
This week I just purchased a Hancock /Hollywood Dun It gelding to be broke and used for trails and endurance. Nothing to indicate he will be a bucker. I hope he’s not squirrelly like the Hollywood Dun It I’d owned previously. What a fruit cake 
The point is. Hancocks are solid and I’ve never had a flighty or broncy one. I’m a once a week trail rider and seemed to have picked good quality horses.
I hear Hancock and I want one
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I bought a Hancock mare a few years ago, as I’m older and wanted something calm for me and my grandkids. This mare was 14 when I got her. She had shown in western pleasure, reining, working cow horse, used for lessons, and was being sold because she wasn’t really suitable for reining, and her owner wanted to focus on that. She is now 21. She is sound, and always has been. She is a super trail horse, is good with my grandkids, and has the lovely trait of not needing to be ridden often to be good.
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Hancocks are rugged big horses who are sound and sturdy. They are not refined types you might show in cases like pleasure. They don’t lend to barrel racing but you never know.
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Emily Miller had a Hancock bred horse make the NFR in 2019. Pretty far back on the papers, yet a bunch of people jumped on the Hancock barrel horse band wagon. eyeroll
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Were they crossing them on TBs to refine them and throw in more speed?
Running bred QHs mostly. I think Emily’s was old school QH on top, going back to Hancock, Two Eyed Jack. Typical running bred on the bottom, Streakin Six, Dash For Cash, Special Effort.
The running QH lines being on the bottom side and closer yet people got excited about the Hancock on the top side. Showing again how much people overlook the mare power.
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The founding sire of the Hancock line was a Percheron. So these horses are all part draft
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Growing up my friend had a blood Bay Hancock horse named Hancock Venture. I think his dam was Roan Lady. He raced foe several years, and did everything for us after that. Amazing horse. Legs like iron
