This argument is flawed as it focuses on a significant but singular need of a child and ignores the child's many other needs as well as the needs of society as a whole. As such at the time of marital separation no protection is given to the relationship the child had with the non-custodial parent, and so in many cases an established psychological bond is broken or diminished. When this happens the child will experience somewhere between mild disadvantages in life to severe behavioral problems. It is well documented how these disadvantaged children score lower in school, have higher rates of incarceration, teen pregnancy, etc. In most states one parent will be awarded sole custody.
Parents have fundamental liberty and privacy interests with regards to their children.
The answers are there is no compelling state interest, and it does not pass a means-end test. An even basic understanding of constitutional law shows sole custody to be unconstitutional. A thoughtful review of all of the options indicates that joint physical and legal custody for all fit parents with established relationships with their children is the answer. This will allow the parents in non-intact families to create the parenting arrangements which are uniquely suited to their child's needs, and their ability to meet those needs. Psychologists have identified mothers and fathers as having different parenting styles, and that children benefit from both.