The PID cycle that controls the rotors, even on racing drones, relies on the gyros to provide the feedback potion of the PID loop. That feedback is "what is the current yaw, pitch, and roll of the drone".

Even in acro mode (which is more accurately defined as "the sticks determine the yaw, pitch and roll rotational velocities"), the gyros are used to measure the actual rate of rotation so it can be matched against the requested rotational velocity.

Positional stabilization, something you see more in the higher end drones, have an additional PID loop that takes input from the gyros, accelerometers and even GPS to determine the input to the underlying control PID loop.