The problem that is solved via high speed sync has nothing to do with the power of the flash and everything to do with the curtain transit time of the camera. Above a camera's sync speed the second curtain begins to close before the first curtain is completely open. Therefore very precisely timed multiple flashes must be emitted from the flash as the open slit between the two curtains moves across the film/sensor plane. Manual flashes are not capable of this precision because they are not capable of two way communication between the camera and flash. The are only capable of receiving a single command to fire.

HSS requires the pulses from the flash to be timed to the particular shutter speed selected and must also take the camera's shutter transit time into account. Transit times and sync speeds vary from one camera to the next. Even if the flash could be manually set to the shutter speed selected in the camera, how would a manual flash with only a fire communication capability know the precise shutter transit time and thus be able to calculate the timing of the pulses needed? Then there's even the issue that one camera's 1/500 second may actually be 1/478 second and another camera's may be 1/511 second.