It will just burn out in the first few seconds and lose its function. Reverse polarity protection is a bit more complex.
Burned parts could also make it easier for the manufacturer to reject false warranty claims.
Another possible diode function: protect the caps from the motor. If supply is disconnected and motors are moved by some external force they will generate back EMF. If it is in the "right polarity", it will only charge the caps. But in the other direction it would damage the caps (or other parts of the circuit). The diode prevents this.
The schottky diode is probably a crude reverse voltage protection, in case the power supply can be connected the wrong way. Should have a fuse then too.Caps have a max ripple current rating, and an ESR rating. It is common to use multiple caps for high peak current demands.Leo..