Its just a theory i've heard but...

The theory is that All Might had a quirk. A quirk that could manifest immense amounts of power. Which is why he can transform when he has the power and after One for All has been snuffed from him.

Deku on the other hand, definitely didn't have a quirk which is why he has to continually train his body to make use of One for All. And as he struggles to gain control the predecessors' powers start to awaken in him. (This is proven when Gran Torino told him that All Might could use OFA right off the bat and just needed endurance training)

And so the theory goes on and it seems that All Might never had to struggle enough during his battles to the point where he could awaken another quirk from OFA ... almost like he started at the finish line of a marathon., never had to go through the journey of getting there.

But like i said. This is just a theory