If I get my hands oily or extremely dirty, Palmolive (which is my go to dish soap) is great for getting them clean, but using on you body will dry you out something awful......Conversely, using hand soap on your dishes will leave them with a greasy/slimey feeling.
I have dry skin and a strick aversion to dishes that don't squeak.......I've had to do both in instances where I was either too broke to have both back in the day or more recently when i lazily run out of one or the other because "fuck going to the store"
Also, I tried using washing detergent in the tub.......It will make your ass itch.
Well, maybe not your ass.......Could be just mine.....But yeah, I had to get off my itchy ass and go buy some bath soap, and no my ass didn't itch before using it.