2 LED strips in parallel dimmed with PWM
Even if the PWM was in sync, the PWM's on/off speed would need to be above 100 Hz or so for humans not to notice the flicker.

Power supplies are too slow to respond to this, the power supply will only see the average of the current going to the LEDs.

For this "slowness" not to be a problem (and improve the response to varying current demands from the load) a power supply will have a decoupling capacitor at it's output and it is this capacitor which will actually take care of the 20 A pulses your LEDs will be drawing.