Why are flash puleses so short?

I was surprised to learn that most flashes last only 1/1000s instead of lighting up for the entire exposure time. Why? If the flash were to light up before the shutter opens and turn off after the shutter closes, there would never be flash sync problems.

Why are flash puleses so short?

I was surprised to learn that most flashes last only 1/1000s instead of lighting up for the entire exposure time. Why? If the flash were to light up before the shutter opens and turn off after the shutter closes, there would never be flash sync problems.