That credit should probably go to Google, and to a lesser extent to Firefox (which at least tried).
Google used the strong weight of Youtube to make sure all web browsers implemented a replacement, a long and tiresome process that took the better part of ten years. They bought companies and gave patents away along the way.
I'm not sure exactly what Apple did. Please enlighten me.
Apple kept Flash off the iPhone, at a time when nearly all web video was in Flash, and when iPhone was the phone to have. There was much gnashing of teeth, but Jobs and Apple stood firm, and demanded the world come to them (which is their way, but in this case what they were doing was for good and not evil).
It definitely wasn't just Apple. Google and Mozilla certainly played a huge role, and I definitely consider them much better web citizens than Apple (Mozilla best of all, obviously), but a lot of sites switched to HTML5 video only because they wanted to be watchable on iOS devices.
Google and Mozilla definitely plaid a supporting role but the iPhone was the main act because it was the device which executives wanted to use. In addition to web video, that also pushed HTML5 in general because all of the IE-only internal apps didn't work on the CIO's new pride and joy.
Apple didn't keep Flash off the iPhone specifically. They made a blanket ban against all scripting languages when they realized they needed native apps after all and opened the App Store.
Adobe could have struck a deal there, given Apple their 30% and only allowed blessed scripts through the App Store. But they didn't. I would be surprised if there weren't neogiations about this, but in the end Adobe refused.
(Other scripting languages budged, which is why you can find Unity games in the App Store, but not Adobe Flash games. Unity was also banned at the same time Flash was.)
So if anyone kept Adobe Flash off the iPhone, that honor should probably go to Adobe itself.
Google used the strong weight of Youtube to make sure all web browsers implemented a replacement, a long and tiresome process that took the better part of ten years. They bought companies and gave patents away along the way.
I'm not sure exactly what Apple did. Please enlighten me.