I use them as a tool (which I find very useful) to look inside the EEPROM at low level. If you are curious about my specific case, I'm implementing a wear-levelling algorithm that includes bit-shifting on the values and that moves the values 2 EEPROM cells forward with every save, with wrap-around at the end. I want to observe what is happening inside and if everything is going according to my plans. Having to wrap my head around little-endianness on top of everything else is something I'd rather avoid, if I can. I also have a function that scans the EEPROM and tells me where the values are and what cells are available for the next writing cycle. For this, too, hex dumps are very useful: if the function sees what my eyes see, then the the function's good.
Your higher-level approach will certainly work, but I work better if I can visualise every cell of memory on my monitor, like a big chessboard, so I can actually see things moving about from one dump to the next. I even went as far as printing a few dumps on paper and drawing circles and writing notes on them with a pencil.