just rewatched Yate's attack. Not saying that it isn't a bit "remarkable" how strong it looked, as he was caught and attacked immediately to gain 10 seconds, but the chasers certainly helped in letting him sail away. From his second attack to top of the hill, the gradient is ~5%. These guys should be going at a good 16-17 mph here, and drafting certainly helps.
At 16.5, Pozzovivo is driving on the front, gap down to 13 seconds (from 18); Pinot second in line, followed by Carapaz. This means that TD is 4th or 5th wheel
At 16.1, Pozzovivo presumably had peeled off from his turn. Pinot now on the front, with a gap to the second rider, Carapaz. Conclusion, Carapaz rode like a twerp and didn't pull through, Pinot got fed up and attacked.
At 16.0, again a paceline, with Pinot leading, followed by Pozzovivo. Everyone presumably has just went over threshold (Pinot to initiate attack, everyone else trying to follow). Gap at 14 seconds, which is insignificant from 13, but soon after, it went up to 18 seconds when Yates crested the hill
All the while, TD was nowhere near the front! From game theory perspective, it's awfully bad faith to be the strongest of the group and not contribute to the chase, especially as the gradient was low here. Gap continued to grow as they dropped into the valley, and finally we see TD working. Yet after one turn, TD has the temerity to tell others to pull through, when he went shirking on the climb...
My take from all this: Carapaz rode like a twerp, but TD was a bit too cynical and was solely concerned about additional energy he needed to burn. He had willing riders who cooperated, but refused to put his nose into the wind until the gap ballooned to over 30 second (12 of which from the descent). The other riders (Pinot and Pozzovivo) were right to shed him and make him work.
Also, at one point they had a graphic showing Yates averaging 420 W on the final incline (~1.5 km from ~3.5 to ~2km). That's 7 w/kg, after 14 days of racing, at the end of a stage, and an altitude of 4000 ft. A lot of power, indeed, but doesn't appear to have anything that jumps out. His ability to put in two attacks though, that was remarkable as noted above.