The phrase "fruitless exercise" means doing something that won't achieve any positive or useful results, no matter how much effort is put into it. It can be seen as a waste of time and energy. Full definition
So trying to get your dog to stop chewing can be a frustrating and ultimately fruitless exercise. (nylabone.com)
but offering to lend money to a Monevator reader is, I suspect, likely to be a somewhat fruitless exercise. (monevator.com)
Notice that the returns you get (intellectual, psychic, and monetary) take years to arrive, and that estimating every day what your degree had done for you would be a fruitless exercise. (thedigeratilife.com)