My assertion is that it is not financially advantageous for the parent to have their adult child living at home.
I haven't made blanket assumptions, by definition, living at home is living with your parents and paying no rent. I am having trouble imagining how it would somehow be financially advantageous for someone to live with me for free if they did not give me money.
Where does this definition come from?
Those that I know who moved back in with their parents post-graduation for a period of time (a few months perhaps, maybe up to a year) were working, taking care of things around the house, as well as contributing to finances (buying groceries, paying for some utilities/paying a portion of all utilities, hell - some even paying some form of 'rent', etc.).
My wife and I moved back in with my parents for a brief period of time upon moving back to an area and not only did we save money by doing so, but so did my parents - their grocery expense was halved, their utility expense was halved, the normal 'every day stuff' was partially/fully handled (we'd do dishes, we'd cook 3x a week, etc.) - it was financially beneficial to both of us.
On top of that, one of the primary reasons for my belief that, if possible, a recent graduate should consider moving back in with their parents is that it will more than likely ground them a little - while they work and take care of things around the house and save money, they are living with people who also work, have a 'boring' lifestyle (work, stuff around the house, sleep, etc.) which will benefit them much more than living with three or more kids who are still stuck in college-mode (blowing wads of cash at the bars, eating out every meal, etc.)
You might believe that 'moving into mom's basement' and playing video games all day is the norm, but I'd wager that you're wrong.