If you truly believe that the measure of amazing programmer is churning out bullshit exercises on a timed call, I can only state that I'm thankful we don't work together. It's incredibly audacious gate-keeping and I'd dare say, discriminatory. It ignores disabilities, social adjustment conditions, etc that wouldn't impact daily work.
I know too many incredible engineers that don't think in the way that those timed exercises require, and these folks are wildly talented and wildly successful.
I do agree with you that the system blocks more people than it should. Personally, I think there should be many more apprenticeships than there are currently. There are many technical roles that can be fulfilled by people of all backgrounds.
But, for the most serious roles, there needs to be skill scrutiny and performance under pressure.
Think of the difference between a performing artist and a music teacher. Both are vital roles and have related but distinct skill sets. The performing artist must have everything drilled and ready to go on stage, much like a heart surgeon shouldn't be doing research on the operating table.
I won't have a great answer since I have no experience in the area. But I would probably ask them to repair something, leave them alone and come back in 2 hours. Pick the mechanic that repaired it the best. I would not stare over their shoulder while they worked.
For the music teacher I would have them record the piece, and send in the best take. I wouldn't demand they get on stage and play the piece.
Are we going to ask a symphonic performer to produce scales during an interview, a heart surgeon to suture a laceration? We would not, it would be insulting for a myriad of reasons.
I know too many incredible engineers that don't think in the way that those timed exercises require, and these folks are wildly talented and wildly successful.