What is the advantage of ozone over chlorine in public pools?

Ozone is rarely used as a primary pool treatment. If ozone is used, bromine is the steriliant of choice, since you only need to add it a few times a year (lower vapor pressure than chlorine). Ozone reactivates the bromine, and is destroyed in the filter. Ozone is hazardous for lungs.

Using ozone tends to reduce the THM and HAA that chlorine can form in pool water. It can also reduce the amount of water "blown down", since fewer chemicals need to be used. And fewer chemical deliveries.

When you turn power off, ozone is gone. Chlorine stays, and stays hazardous.