I believe that a father should know if they are the parent of the child. Too many times I have seen fathers get floored when a child became ill or hurt and the fathers DNAs didn't match to give blood or was told the illness was an inherited illness and not from the mother, such as sickle cell.
It would help, also, when trying to get child support. Most fathers try to say the child is not theirs and the courts have to wait for the ordered blood tests to see if the child belongs to the man or not. Another case I remember was when the mother was trying to get TANF in her state, the father lived in another state, and blood tests were ordered. The father sent his brother in for the blood tests instead. This trick happened because both boys looked exactly alike but were two years apart. Needless to say, the mother was turned down for TANF, food stamps, and medicaid causing her to place her children in the foster care system until she found a better paying job.
Therefore, it is wise to do blood tests immediately after birth.