So it seems It's a win-or-lose situation whether you buy a seat or you don't buy a seat, just a better chance getting a guaranteed seat when paying for it.
What I can't understand is if you paid for a full-fare ticket for your child why is he getting bumped from his seat, the airline knows how many seats they have that was purchased ,why were they over book a flight knowing a few people are going to have to go off the fight?
I would suggest that maybe they know about a few seats where infants / children are occupying it and can get an adult to sit there instead of the child , but then again if your booking your child has a 15 year old or 10 year old there's no way to know if it was booked for an infant.
If an infant paid for a seat why does an adult get priority over an infant ,the airline's are not losing any money as that seat was paid in full?