Weight, breakage, flexibility and space constraints for dishes are much different
Also, someone needs to scrape, check, pack and unpack the boxes. I can't see this saving money, especially at places with high turnover.
But if there aren't enough dishwashers, then the ones that they do have quit because they're overworked, then the rest of the kitchen staff has to pitch in and THEY are overworked too, and then the customers get slow service, it's like dominos. I can see just falling back to dish delivery