Remember that, if you make it a job, you're no longer free to decide how you want to raise your children, what values to teach them etc, you're now just a caretaker that produces a labor source for their employer. I'm not sure that's such an attractive thought.

There are a lot of self employed that have freedom on how to do their work. We could see it as self-employed contribution to the future of society. Also raising new citizens with a diverse set of values & beliefs is exactly what I would want to see. It would be horrible if their was some kind of institution that would dictate the same kind of upbringing for every child. However, in the end parenting is really not a job even though it provides value to society. That doesn't mean it doesn't have to be financially supported just because it is not like the kind of work that typically gets paid.

Self employed people aren't disconnected from society though, they don't "work for themselves", they still need to offer something that others consider to have value. I don't think we want parenting to be judged in that regard, it does very much change the relationship between the individual and the state (and not in a good way imho).