Some people don't consider the economics of having kids before they commit, but it really is an economic decision. People have fewer as the opportunity costs rise when wages rise and as retirement depends less on your own adult children. Whatever changes occur in the market are reflected in how many parents will supply, but this is one area in which government intervention is common place, particularly when state governments regulate child custody and support payment laws.
When a couple splits, they theoretically have joint custody over their children, but many times the mother gets the child regardless of either parent's fitness. I know this personally, because when my parents got divorced, my father was told he could get custody if my mother had ever committed a felony, if she had been adjudged insane, or if he was willing to plant evidence. I have heard that this was not always how it is now in Colorado, but I read this: http://drhelen.blogspot.com/2008/09/i-refused-to-settle-for-becoming-disney.html and it looks like that's not the case in every state. As that blogger writes, "...it makes me think that if Baldwin had such problems with the system with all his fame and money, what chance does the average joe have?"
Transferring custody away from a parent who hasn't committed a crime is a violation of his (or sometimes her) right to private property. This could be settled much more efficiently and freely with contracts between the two parents, with government only enforcing their decision. Then government would not have to know what was best in every case because the people with the knowledge for it could do it for themselves. It actually seems to me that it would probably end more equally as one parent wouldn't be forced to give way to the other by coercion.