This is pretty much the idea. We used this method when I was a kid growing up BAC. (Before air conditioning.). Although, kudos to all who thought swamp cooler was the name of a cocktail. If it already isn't, it should be.

You put the ice in containers/buckets in front of the fan. Could be helpful if you close yourself off in a small room, if the central unit is out. But takes a lot of ice, which costs (your fridge couldn't make enough ice to keep that container filled for hours).

I also used to have a small white (to match the walls) window a/c in a back or side room (where the a/c doesn't show at all to the street or other people), to use in emergencies or to close the door to keep just the bedroom cooler while central unit temp is turned higher for the night.

During the past 4 or 5 years it has gotten a lot worse and I finally broke down and got a small floor A/C unit 3 years ago and it has saved my sanity. Electricity is very expensive here too. Also, not many people have them since we live on the West Coast which is supposed to be cooler due to the cool Pacific. We have definitely seen a big change in a short time.