How can you say that? Look at the up and coming QBs: Mahomes, Allen, Murry, Jackson, even Tannehill and Herbert to a lesser extent. All are more adept at running than say Brady, Brees, Rivers, even Big Ben. In addition to being good to great pocket passers, they can escape the rush, run for a first down, or throw well on the run. Rodgers has always been a "tweener", more adept at running than Brady, et.al., but less oriented to run than the newer breed of QB.
I am not saying a pocket passer in the right system cannot be great. But the paradigm has shifted from that being the rule, to the exception.
Edit: If by "running" QB, you mean run first, like Jackson at Baltimore, I might agree with you.
But that is not what I am talking about. I am talking about being able to at least run effectively if the protection breaks down, run for a first down or throw on the move, and maybe occasionally do a planned run.
For the criteria in your last paragraph, Big Ben was probably one of the best QBs to give defenders the slip in close quarters behind the LOS. In the batch of recent QBs, I would say Watson is the QB most similar in style when it comes to making crazy escapes behind the line of scrimmage like Ben. Mahomes is greater in a lot of things, but as a "dancer" behind the LOS, Watson and Ben have him beat.
I barely followed Ben but the few times I've seen, it's enough to show that his ability to escape is rare. Heck, he triggered my PTSD this season when the Washington blitzer had him dead to rights right up the gut buuut, the blitzer missed and he was set up to make a throw.
Aaron Rodgers is pretty capable of everything listed in that last paragraph except maybe the designed run.
Steve Young is in the HOF and people knew he was a terror in all aspects.
There have been plenty of mobile QBs who simply did not reach expectations or circumstances killed their mobility. Since they failed to do so, they have been forgotten. Alex Smith actually was quite the speedster, but having a revolving door of coordinators in San Fran did not help his development. His replacement, Kaepernick, was basically Greg Roman's first foray into making a one-dimensional running QB work.
In addition, very little attention is paid to a white QB's mobility even though they are measured.
Carson Palmer actually ran a 4.62 40 and hence mobility was part of his prospect package. But injury would kill that part of his game and then he got the stereotype of "traditional pocket passers".
Christian Ponder and Tarvaris Jackson are both forgotten busts but they both ran sub-4.70 40 times, with the white Ponder actually .04 seconds faster.
Vince Young was the speedster of his draft class, and Jay Cutler had enough mobility to scramble at 4.77 seconds. Mike Shanahan loves his QBs to have a little roll out ability, so Cutler passing his eye test is no accident.
Sam Bradford was also another understated athletic QB. He had to suffer with no Oline as a Ram, so injuries shellshocked him. His draft peer was Tebow, and "genius" Josh McDaniels thought he could make a QB out of him. The same Josh McDaniels who coached Tom Brady for years.
Likewise, in Cam's draft class, the white QBs in that class were also very athletic. Jake Locker, Gabbert, and the aforementioned Ponder all had sub-4.7 40 times. They all happened to bust out of the league while Cam did not. Even though Andy Dalton has a paltry 40-time, when the game is one, you can see he got little scrambler in him too.
Andrew Luck could run, but again, no attention was paid to it by outsiders. Now that he's retired, he's been quickly forgotten.
Johnny Manziel had run a 4.68 40 time but we know his story...plus no one gives a crap about the Browns...unless it is Lamar taking a crap during a game against them(I just had to put that in.)
Geno Smith is another.