Once again: for a social scientist, marriage is a nexus of commitments, personal, social and legal; marriage vows are only important inasmuch as they contribute to those commitments. Hence one can easily imagine a society where de-facto and de-jure marriages are indistinguishable. As I understand, Sweden is close to it.
The word “illegitimacy” should be banished from use in decent society. Thank God it has been, here in Russia, since 1917. One of our few advantages. There should be nothing illegitimate about bearing a child, ever. (Unless there is severe overpopulation — but the child shouldn’t have to live with the brand.)