Who decides what good parenting is? Bonding and love are so important, especially in the early years, that no training can substitute for that. How well can the state judge one's capacity to bond with and love their child? How well can an institution judge that? In fact, it may very well be that this capacity does not truly reveal itself until one becomes a parent! Love, providing a child a sense of security of love and support from a parent can override any other consideration that might be involved in the training and licensing process.
And if a person is determined to be objectively unqualified to be a parent, what happens then? They're not allowed to marry, not allowed to bear children? Talk about big brother! And based on institutional and governmental track records in managing such things, I do not think it would at all be a good idea to have the state, or some institution deciding who can marry and who cannot, who can bear children and who cannot.
Or forcing abortions on couples who have conceived a child contrary to big brother's edict.
No! to licensing of parents, but yes to supporting families in all possible ways, including education, in order to promote better parenting.