The bottom line is that the primary role of the NFL QB is to deliver the ball, mainly from the pocket, to open receivers. Necessary skills to accomplish this include: understanding the playbook inside and out, reading defenses, quickly going through the progression, being able to see the open guy, making the right decision of where to go with the ball (or to just throw it away or take a sack), and accurately delivering the ball.
There are many places throughout that chain where the play can break down for the QB. Maybe he is good at lots of things but panics in the pocket and/or lacks the proper footwork leading to bad pocket presence (RGIII). Maybe he has a tendency to not see open guys (Ben Roethlisberger). Maybe he is the perfect physical specimen but lacks accuracy or touch (Christian Hackenberg). Maybe he has everything else you look for but regularly makes bad decisions with the ball (Jay Cutler).
The problem with a lot of these mobile QBs being drafted now is not they are "mobile". Mobility in and of itself is never a bad thing. It helps any QB -- AS LONG AS they already have the skills necessary to succeed if you were to take the mobility away. Russell Wilson, Aaron Rodgers, and Andrew Luck are mobile QBs. But they have all the other skills necessary so the mobility just makes them better.
In college, a lot of QBs eat off their mobility but at the same time it masks their deficiencies in the areas necessary to succeed as an NFL QB because the college game is different. But because they were SO successful and SO hyped, teams are afraid to pass on these guys, knowing they lack certain skills, because they don't want to be the team that passed on a future star (even if the possibility is remote).
It may be for others, but to me it's not even a race thing. Johnny Manziel and Tim Tebow are two QBs who would never have been half the players they were in college without their running ability. They got drafted high because of the hype, and then Tebow was exposed. Manziel hasn't been yet, and as much as I love him for elevating my school to new heights, the odds are against him too. I will say he has much better arm talent than he is given credit for and is deadly accurate. But I'm not sure he possesses the decision-making ability required because he is so used to relying on his scrambling and/or throwing it up to Mike Evans.
The NFL game has changed in a lot of ways, but one thing that will probably never happen is "running QBs" who lack pocket passing skills surpassing the guys that do have those skills at an elite level.