I suspect the FAs have no power because it's not their baby, and it's not really their job to tell the parents how to take care of their own baby.

How are they supposed to do it? Tell the mom "you can't do this and you must strap your baby down"? What if she says "I don't want to"? What is the FA going to do? Force her to? Threaten to kick her off the plane? There's nothing they can do really.