Half those arguments could be made for child labor. After all, if the child works too then the family has more resources, the father and mother don't have to carry all the weight, the child gets a wider variety of experiences, the father and mother can do something that matches their talents while the child picks up the slack. Right?
Who actually cares more about a child's well-being, an employee paid by the hour or their own parents?
I would not say that the child gets a wider variety of experiences in child labor compared to child care. Child care is explicitly designed to have a variety of activities for children. Child labor is the low skill kind with lots of repetitive actions. Child care also takes the child's needs into account, like having nap times and eating times designed around children, instead of around a production process.
As for caring about the child's well-being? The parents, which is why they should hire the best people they can afford to do various parts of taking care off them. Hire the best doctor for their medical care, hire the best dentists for their dental care, hire the best teachers for their education, hire the best child-care professionals for daycare.