The Chiefs of the early 2000s weren’t a ball control team either. Holmes got plenty of carries, but Trent Green was also passing for 4,000 yards on an annual basis (despite never having a #1 wideout, or even one who’d be a top-tier #2 for that matter).
When I think back at the long runs I remember from Priest Holmes I realize many of those weren’t runs at all but screen passes. They had one of the most active offensive lines I can recall. It was fun watching them, especially in the red zone.