Why do Boeing planes have more flap settings than Airbus planes?
And some older Mooneys have infinite flap settings depending on how much you pump them up...

The reality is that there are no regulations on how many flap settings an airplane must have and on an airliner that may also have things like speed breaks or slats as well, flap settings may vary by design or simply by engineering choice.

Flaps are used for improved short field take off as well as to make a steeper approach at a slower airspeed. If Airbus can achieve desired performance with 4 settings there is no need to complicate matters and add to pilots work load.