Prescott and Watson are not running QB's. Both are good passers.
Jackson/Vick/Cunningham are/were not good passers.
To understand this, you'd have to make the distinction between running QB's and Qb's who can run. The QB running is not the problem, the QB running too much and not being a good enough passer is the problem. Quite simply, a QB who depends on running the ball himself is too one dimensional. Against good D's, those type QB's get exposed.
One of the problems is that after a QB has taken off and run a good ways, he's huffin' and puffin' a bit, and this throws off his passing for a play or two, sometimes a series.