Path: No flashing. Light up to see where you are going and for other cyclists to be able to see where you are.
Dark road: No flashing. Light up to see where you are going.
City street at night: Flashing and solid. Flash to get attention, solid so drivers can judge distance.
City Street in daylight: Flash to get attention. Motorists can see you but may not notice.

The main problem with having just a flashing light is that it makes it hard for cars, pedestrians, and cyclists to judge your speed and distance.