The buster call that targeted Egghead would have been easily wiped out by the straw hats and giant pirates if the Gorosei weren't' there, and that's including Kizaru. Hell you literally had to have things happen constantly to keep Luffy, Zoro, Sanji and Jimbe away from the buster call for it to...
Given the mural in Elbaf it's pretty possible Roger learned this on Laughtale, and it was yet another reason he started the great pirate age.
The theory is one of the things where it makes perfect sense, but if it didn't happen I wouldn't mind either.
Gear 5's "time limit" is plot dependent. He fought Kaido in the form far longer than Kizaru. None of their classes were even close to those with Kaido or the Gorosei.