There is some reason about why child isn't covered by their insurance.
1) Some companies don't offer plan that cover child
2) The insurance to cover child is very expensive, for my father's workplace, the insurance cover child cost $890 per month, that take more than 50% of his paycheck. The insurance to cover child is usually cheaper if you work at medical care or insurance companies but not all of them.
3) Many companies don't offer insurance to part time workers, especially some people have 2-4 part time jobs, that's very unfortunately about they couldn't find a full-time job with benefits. Some companies kill benefits for full-time workers.
4) Some parents are irresponsible, that's not common as few listed above.
ACA fixes the problem for child and the families can get insurance at cheaper via exchange instead of workplace.
The skyrocketing of medical care have put companies to change the benefits, that hit child so hard.
Previously, most young adults were uninsured but it is mostly resolved by require all insurance to cover young adults until 26 years old.
The insurance companies are partially contributed to medical care problems.
I do understand your post Foxrac. But the central question is: Should not people resolve these situation BEFORE having a child brought into the world?
There is too much apathy among the population that just "shrugs" and says "not my problem, people have a right to sex". However, these same people don't realize that THEY pay the consequences for a child brought into the world by these irresponsible parents. Once these people realize (might take a slap upside the head) that THEY are responsible and suffer the consequences, then THEY will get busy speaking for a stop to these irresponsible acts.