A guy my dad worked with did not know he had a child until the kid was grown. The mother waited 18 years to tell the guy and file for child support.
The man was in his 50s when he found out he owed 18 years back child support, totaling close to $100k.
But yet, somehow that is a fair and balanced system?
Anecdotal evidence.
What would be a fair system, is for both parents to be held responsible for caring for the child.
If the mother can drop a child off at a safe harbor, then the father should be allowed the same rights.
Both parents are equally responsible for caring for the child at all times. If a mother drops off the kid at a safe harbor, the father is not responsible for continued care either. What you are advocating for is clearly a logical impossibility the other way around, as most women tend to notice when they give birth to a child.
If a mother does not want a child but the father does and takes custody, she is every bit as liable for child support as he would be the other way around. Again, all parties share equal responsibilities at all times.
If the father is court ordered to provide health insurance and pay child support, then the mother should be court ordered to get a job and provide health care.
The system is tilted in favor of whoever has possession of the child.
That doesn't make any sense. One person is actually raising the child, the other is not. The purpose of this system is to provide the greatest care possible for the child. Period.
I fail to see how any of your solutions improve this.