QBs are the most protected player on the field.
However, running QBs by rule give up much of that protection. The minute they take off, they are a RB according to the rules (I suppose the exception is the slide).
The reason good QBs could play well into their 40's is that protection and that barring physical problems, they tend to get mentally better with time even if there might be a slight drop off in physical skills.
Running QBs, on the other hand, are a different animal. They get clobbered so 20 year careers are not feasible for them. In fact, other than for the rare case, running QBs have pretty short NFL career spans. Should they try to change and stay in the pocket and become a pocket passer, it doesn't work because they never developed that kind of skill and its not their instinct. They've been running QBs since elementary school. Stopping running because you're now afraid of getting hit more doesn't work. Wilson will never be the same if he stops running.