HTML5 just provided a suitable replacement for Flash, but suddenly having a large browser (Mobile Safari) that just couldn't play Flash content at all provided the incentive for web devs to actually invest the effort to switch to HTML5.
This is the correct answer. To add historical perspective, I had friends who would go into Apple stores and point all the demo machines at newgrounds.com to show people that they shouldn’t waste their money on devices that couldn’t even play flash animations as well as a low end laptop.
HTML5 just provided a suitable replacement for Flash, but suddenly having a large browser (Mobile Safari) that just couldn't play Flash content at all provided the incentive for web devs to actually invest the effort to switch to HTML5.