You can trace it back to Tebow or credit Meyer. Instead of treating the QB like a Faberge egg sitting on the mantle, not to be touched or breathed-on too harshly, you utilize him as a ball-carrier, using your ball-carrier as an extra blocker. Coaches have always wanted their QB to be big and strong as a defense mechanism from being hurt by traditional methods (getting sacked). Meyer said f- that, if he's big and strong, let's USE that proactively, as an offensive mechanism.
So Tebow did it and was okay (he was hurt that one time on a pass play), Newton did it and was okay (and was Tebow's backup initially), then even little Johnny Football did it and was okay. So as all good ideas do, it caught on.
There's nothing wrong with handing the ball off to a RB. But if a player (QB) takes on more of the workload, it should be taken into account, and he has, will, and should be credited for doing so.
These offenses that didn't have a FB, but recognized that in certain situations, you are best served to have a FB, you use the biggest guy in your backfield, which is now often the QB. There were Michael Vick and Pat White types, trying to take advantage of their speed, but those were mostly (if I recall correctly) the traditional draws and scrambles, with a few option plays thrown in.