Yes, people will point out that there were plenty of running QB's out there who played well back in 80's, 90's, etc., such as Steve Young, Randall Cunningham, etc., but there are several things to take into account.
1) Nose tackles back in those days rarely were heavier than 290 lbs. Michael Carter and Ted Washington were probably two of the biggest guys in that era at that position. Today's NT's are well over 300 lbs.
2) 3 technique tackles were usually around 275 lbs (no joking). If you got heavier than that, you were thought of as being too big and slow for the position, and would be shifted to NT.
3) Strongside defensive ends were closer to 260 lbs, and seeing a monster the likes of Reggie White or Bruce Smith (both of those guys were around 280) was a rarity. These days, that kind of weight is more of a weakside end's.
4) Linebackers were around 230 lbs, not the hulking 245 lb nightmares you see today.
5) Safeties rarely cracked 200 lbs. Someone like Mark Carrier was closer to 180 lbs, and a 200 lb safety the likes of Ronnie Lott was extremely uncommon. These days, safeties are around 205 lbs.
That, plus all defenders look like they're bigger, faster, and stronger than the ones from 25-35 years ago. Combine all of the above together, and today's runners are getting beaten up much more than they were a few decades ago.
This is why a lot of running QB's who were spectacular in high school and college either have very short lifespans in the pros, if any at all. You won't see someone like Tim Tebow out there.
Cam Newton is probably the best running QB ever seen, and frankly, I'm surprised he lasted that long.
He's big, strong, fast, and can also throw decently. Back when he was at Auburn, he could run over any safety, get the better of just about any collision with a linebacker, and even shrug off hits from the linemen, and keep on running.
In the pros, even at 250 lbs of solid muscle, he's like an old man out there, since he got battered and bruised senseless throughout his career, and you can see how badly (and quickly) he declined after his one big glory year. Those hits do add up, and painkillers can only cover things up for so long.
Riley Leonard, if given a chance in the pros, would get eaten alive if he doesn't learn how to be a passer first.