When ceremonies backfire

Last night, Builder and I went to my nephew's pidyon haben.  (As in, my nephew was the baby's father.  It's about the only time that it registers that Builder is older than me.)
As my nephew redeemed his new son from his uncle (who is a Kohen), I had to wonder--what would the Kohen do if the father said, "You know, I'm not really ready for fatherhood, and taking care of kids is more than my wife and I can handle right now.  You take the kid, and I'll keep the coins."
Now, I've only seen about three of these in my life, because they're extremely rare.  However, this is a serious ceremony that means something!  Parents are actually asked if they want to give their firstborn to the priesthood!  There is a chance that a parent my take the Kohen up on his offer!
It's like the chalitza ceremony.  A few years ago, I saw a TV movie called Loving Leah.  It was about a man whose brother became a BT, married a frum girl, and died young and childless.  The secular brother had to show up for chalitza.  However, he felt guilty about cutting off his brother for so many years, that he ended up marrying his sister-in-law.  Weird premise for a movie, but it proves my point.  These ceremonies actually mean something.  I'm sure that at some point there were parents who gave up their children to the priesthood, either out of poverty or some kind of "safe haven" because they were overwhelmed.  Like dumping newborns off at the firehouse.  A little something to think about at the next pidyon haben.