You are right. But, I know that in my case we took a child in that was a ward of the court (she was a family member). We could have taken a monthly allowance from the state along with her. We chose not to take the money.
Likely because you realized you could raise the child without the allowance. Good for you for not taking what you didn't need. In addition, you probably freed yourself from a level of governemnt oversight and inspection on how the money would have been spent.
In my mother's case, she simply outspent the insurance settlement she received when my father passed away. Dad was always the one that told her not to spend so much and, without him, she spent til she had almost nothing.
She didn't even know Dad when he was a soldier in WWII. But she (actually, us children) are getting the benefits from the VA and not the one who "earned" it.
Our family (myself included) still has to pay some of what it costs to keep her in good care but there's no way we could give her what she needs without the benefit. It bothers me to some extent but it's a family decision and I've reconciled my conscience about it.
When my turn comes, I'm not going to want a dime from the government.