With the birth of my second child, I had to exhaust my sick leave during the disability period immediately following childbirth. While my son was a newborn, my husband began experiencing serious sensitivity to sound, which turned out to be a component of undiagnosed autism. As a result, he can no longer care for the children alone and we have to pay for additional childcare.
Since I returned to work, both children and I have been ill and care for all of us falls to me when a child is ineligible to go to day care. Without sick leave I have been informed that I will have to take any sick days as unpaid time.
The biggest thing I learned from all this is that burning through your leave in order to spend time with a new child is a luxury, but also a decision that will take years to recover from both in terms of accruing further leave and dealing with the expense of unpaid leave.
It is in the best interests of society for parents to have time with their new children, and this is very often financially impossible.