"If hiring programmers who aren't good at programming puzzles is a competitive edge, I would expect to see other companies hiring these programmers and succeeding."
You're begging the question. Other companies do hire people who are excluded by a certain class of employer, and that's exactly why some get outraged by the types of quizzes that are used. The difference between the standards creates cognitive dissonance over one's ability and status. It's effectively a caste system, and it involves persistent blind spots about discrimination, whether towards protected classes or not.
I can't pass an Amazon or Google phone screen - both of them invited me to try, and they then made me feel very out of place. I'm not a software engineer per se and I didn't get my CS degree from a top school. Yet I have worked for a company that Google outsources important work to, proving I can do useful things that Google needs done and maybe isn't even able to do in house.
I don't go around raging against Google hiring who they want, partly because I'm probably better off not working there anyway. But I understand where people are coming from when they do get angry, even if it is the sign of an imperfect character.
From an employers point of view, they just want to grab the employees that are suitable for their goals and jettison the others. But from a potential employee's perspective, it seems like if I'm not good for one job at a company, I should be good for another. Rejection seems unreasonably total. If, by analogy, you deal in second hand cars, it's a reasonable business model to buy virtually any car so long as the price is right and you know who to sell it to. But not all businesses are run like that of course. It aggravates people that there is a narrow vision for who is useful.