What do your counterparts at the company think the source of their hiring difficulties is? If not flawed process?
But when you reach the final stage with 3 people who you know can pretty much do the job, who you know have successful careers working in successful companies, and you drop them because they didn't exactly behave the way you would prefer them to in a high stress scenario, and keep looking, I think you effectively forfeit the right to claim that's your problem with hiring.
I didn't think of the solution you had in mind, because I've identified another problem that you didn't consider. And somehow that takes me out of the running. Good luck with that.
Not to mention the nebulous and vaguely discriminatory "cultural fit" problem. So, even if I manage to ace the technical, I still fail.