I don't see the need for a halter bred horse to be a barrel racer, but a horse that is correct enough to run can race barrels.
I wouldn't ride a horse with awful conformation, let alone run barrels on it, but most horses at local shows aren't anything special..
Not saying this horse has awful conformation.. The second Picture, she looks really good, actually. I also don't see the high withers.. I think, she is just standing funny in that picture.