Should nominal or stall current be used for power supply selection for BLDC?
If you are starting up under load with no soft start, I would use stall rating since stall current is what your motor starts up with, even if you never really plan on actually running near stall. Something that starts up under load is a wheel or conveyor belt. Something that does not start up under load is a fan.
What capacitors do is smooth out power dips the motor causes for other things sharing the power supply with the motor, and to provide the high frequency current demands of the BLDC driver (since the power supply won't react fast enough due to inductances). Those last two things I mentioned are actually the same thing.
They probably are not big enough to support the motor itself if the motor truly exceeds the limits of the power supply for any noticeable period of time.