Most “running Qbs” need the run element of their game to be any good. According to your own analysis, Newton and Wentz require the running elements to function. None of them are pure pocket QBs because they lack pure pocket skills.
Murray, OTOH, thrives in the pocket. If he didn’t run, he would be considered a pocket QB based on his ability there. Running is not necessary for him; it’s just an added threat.
If he needs to become less mobile for health reasons, he should have no problems adjusting and it won't hurt his game.