You don't need the 50 rush yards a game quarterback but if they have to and can that only helps your team, especially if the run game isn't working that day. But you do NEED a QB who can get outside of the pocket to extend plays, run for 1st downs when plays break down, or be a threat near the goal line to take it in.
This years playoffs:
Lamar Jackson, mobile
Josh Allen, mobile
Patrick Mahomes, mobile
Jared Goff, mobile
Matthew Stafford, not mobile but extends plays with getting out of pocket and moving in pocket
Jalen Hurts, mobile
Justin Herbert, mobile
Baker Mayfield, mobile
CJ Stroud, mobile
Jordan Love, mobile
Jayden Daniels, mobile
Sam Darnold, surprisingly mobile
Bo Nix, mobile
Russel Wilson, mobile
NCAA CFP National Championships:
2024: Riley Leonard, mobile - Will Howard, mobile
2023: JJ McCarthy, mobile - Michael Penix, mobile
2022: Stetson Bennett, mobile - Max Duggan, mobile
2021: Stetson Bennett, mobile - Bryce Young, mobile
2020: Justin Fields, mobile - Mac Jones, not mobile but extends plays with getting out of pocket and moving pocket