You sound like someone I would not like working for. And that, maybe, is just as valuable as anything else. You've got a process that identifies the type of person you've had good luck with in the past. Your process also identifies you as the sort of person I've had bad luck with in the past. It works both ways. You're missing some excellent developers who maybe are not articulate at the whiteboard but do fine at the keyboard, even under pressure.

If you think this is "draconian and insulting", just wait until your knee deep in digital shit with customers barking at you all day long.

How many times do you have your customers in the office, throwing out arbitrary programming challenges for your developers to solve on the spot at the whiteboard?

It's fine if your methodology works for you, but you might consider that it's not the only approach that could work.