Would using an old refrigerator that takes blocks of Ice as the refrigerant be better for any reason?

I know they used to use fridge’s where you put a big block of ice at the bottom and replaced it every so often. All your stuff stayed cold, and I guess it did not use electricity. I don’t know how these worked, but it seems better than running electricity all the time to a fridge. Is there anything redeeming about those old fridges that would make them come back worthy?