To be fair, a toaster is always a fire risk. That's why the manual says never put them under flammable things. You should always assume your toaster will catch fire.
You only save money if you plug it in afterwards. At which point residue poses a fire risk.
Also, many dishwashers have a garbage disposal which isn’t inside the water and may fail if the cord gets into it. Not likely to happen, but enough people try it and someone may directly get an electrical fire while the dishwasher is running.