Josh Allen runs all over the field. Pat Mahomes does, Lamar Jackson, Kyler Murray, Kenny Pickett, Geno Smith, Russell Wilson, and Joe Burrow will run around a bit too. The days of Tom Brady and Peyton Mannings sitting back in the pocket and shredding defenses are over. You gotta be mobile nowadays.
This isn't a black and white issue in my opinion. The best quarterbacks are pass centric first. They can distribute the ball to playmakers while limiting hits to themselves. Tom brady, Matthew Stafford, Joe flacco and Peyton Manning come to mind. None of them can run for s***.
A few dynamic quarterbacks are passers, but also have an ability to run it, so it would be stupid to not have them pick up some yards here and there. Think Josh Allen, Patrick Mahomes, Russell Wilson and Steve Young. They keep drives a lot that lead to points.
Then there's guys like Michael Vick and Lamar Jackson. They can pass reasonably well, but we think their tendency is to rely on the strength of their running, to the detriment of their team. If their first instinct is to run when things fall apart, that is not a recipe for championships. You'll win a lot of regular season games, but the best defenses will hem you in deep in the playoffs. Good passing is such a requisite within the red zone. Not entirely, but you rarely take it into the end zone without completing some passes.