People's lives change, and not always in a positive way.
So, what if you have 3 or 4 kids in a loving family. The father was the main bread winner, and he dies. Or perhaps he just meets someone else and leaves you? Or he could lose his job and struggle to find a new one, or perhaps he has an accident, or gets cancer, and can't work? What if a family member gets ill and you have to care for them, and can't work as many hours? What if you had a good job, but the father leaves, dies or has an accident/illness, and you have to give you up your job to look after the kids?
Would you feel happy telling anyone in the situations above that, although there's a minimum amount that the government thinks they need to provide for their children, they won't get it? To me, it sounds like most of those situations are exactly where we should be stepping in and providing support.
And if you think that we instead have some rules to separate out the more undeserving parents, then you're on a very slippery slope, and you'll soon discover that people have very complex lives, and you'll struggle to define rules that could ever be objectively "fair".