That was the #2 cause of "joystick not working" problem on the C64.  While most games worked in Port 2, some were Port 1 and all you did was switch ports.  I didn't have many games that had 2-player simultaneous action.  So most of the time we'd just swap.
FWIW, the #1 cause of "joystick not working" was too much Epyx Summer/Winter games and/or Decathlon.