I wonder what percentage of the job space truly depends on the current edge we have over machines.

I think it's reasonable to worry that way before machines are more reliable than the average human (let alone more reliable than a highly trained human) they can pose a significant disruption to the job market which will send shockwaves throughout society

That is why we need functioning states -- free markets won't save you in such a case. Though I found it is hard to explain especially to U.S. people, who put "regulation" on par with f words :)