Who's they for the first minute though? It's not that Carapaz didn't put in efforts to get back to Yates, just didn't work. You can say del Toro was being an idiot, but I disagree about Carapaz at that point. If anything he attacked to much and should've gone up a more steady pace, but than again that's not exactly his style.
Yates was hanging a few seconds in front of them for quite a while before they started playing games with each other. Then Gee started catching and riding past them as Carapaz kept trying to get del Toro to ride so that he could attack him. If they ride together, or if Carapaz is happier to ride to tempo and worry about breaking del Toro later rather than getting impatient, then that gap doesn't open up as rapidly as it did.
Once there was an established gap, Yates proved that he was the strongest man on the day and would likely have got away anyway, but it might not have been a decisive margin, certainly not enough that the two behind gave up so soon on the final climb.
A bit like how David Arroyo was only about 40" behind Basso, Nibali and Scarponi at Edolo, but over 3 minutes back in Aprica, because he just couldn't get any cooperation from the likes of Vino and Evans who he'd caught and passed on the descent, and so the easy climb built up as big if not bigger gaps as the harder one before.