Its a travel scam. I read about it on a message board for flyers. They were all saying how they do it. I don't have the link. Read about it a few years ago. This is roughly how it works.

1) Buy refundable ticket for small child.
2) Book child's seat right by yours.
3) Carry on child, but then don't give gate agent child's ticket.
4) Put kid in seat that you booked, but didn't scan.
5) If they try to give away seat, claim that you "paid for" the seat, but the gate agent must have scanned it wrong. Show it to gate agent and claim you handed it to them.
6) Blame the airline and make a big deal on social media.

It all works if the flight isn't full. It also works because the CSR won't question you carrying a small child assuming its a lap child. The goal is to block the seat from others. Someone tried this exact same scam on Delta and they caught it.

Delta Flight Kicks Family With Toddler Children Off Plane | Fortune.com