Should not, and do not aren't always the same thing. The AMD RX480 series at release drew signficantly more than the 65W of 12V from the mobo they're allowed to. The total for an x16 is 75W, but 10W of it is 3.3v power (to facilitate porting legacy parallel PCI devices which ran on 3A@3.3V power).Yeah, I know that's how it's supposed to work, but the point is... I have seen low-end motherboards struggle with high-end graphics cards before, and seen power supplies that can run a card in one motherboard not able to keep it powered on another. Maybe there's some other reason and it's not the power delivery or the VRM, perhaps I was wrong on why it doesn't work. It could be some other aspect of the design, like lane speed or how many layers the PCB has, I really don't know... but I still am convinced it's not a good idea regardless of the fact that it should theoretically work.
This article I found from Toms shows a card they tested drawing an average of 85W of 12V through the slot with short peaks as high as 168W. This originally came to light after a few people with low end mobos actually burned out PCIe slots due to over-current while gaming. AMD eventually released a driver (firmware?) update that reconfigured the cards to draw more power though the PCIe power connectors and less from the mobo.
https://www.tomshardware.com/reviews/amd-radeon-rx-480-polaris-10,4616-9.html
https://www.reddit.com/r/Amd/comments/4qwzpy/three_motherboards_and_counting_have_died_from/