happy mum = happy baby.
There is so much more to it than that. It's a lazy catchphrase that seems to be shorthand for:
"I can't be arsed helping you with your problem, go for the easy option."
Parenting decisions go deep and feelings about them last for a long time.
e.g. MIL still feels guilty about doing CC on her middle son, 30-odd years ago. She thinks she would have been better advised to have fed him when he cried...
People come to MN with problems that may have many causes. Either try and winkle these out of the OP, or shush.