They don't need a volunteer. They can clone themselves when they are, say, 30 year old and they will have a 100% compatible, 20 year old donor who has spent their life in suspended animation when the original is 50.
Then, one day, the are told their important and distant "parents" are finally arriving to bring them away to their new life...
Anyway, the point is that any aging wealthy pedicidal murderers are also gonna insist the body is perfect before they move in. The easiest way to do that without conjuring more new technology is the force the future-victim to do it.
And you also reminded me of the flawed but moving film "Never Let Me Go" from 2010 about a more present version of this. Oh, and there's also Michael Bay's "The Island".