“Legalization” of marriage results from legal history. The term “license” seems like a misnomer to me and I don’t know why they ever called it that.
US law is not solely based on the constitution. Civilly it is largely based on English common law. This ties into the constitution in regards to property rights.
So what happens to “your” property when you die? If you think property belongs to the state you might support big inheritance taxes. If you think it belongs to the individual you think it belongs to their family.
So how does the state “know” who that family is? The only way is if marriages and births are recorded.
Hence I always thought it should be called a marriage recording fee as opposed to license.
It could be that the original intent of “license” was a deliberate way of excluding what the entire history of civilization knew - that it was between men and women, even in the polygamous societies, and did not include same sex.
A libertarian would say that the state does not need to know who the family is. The Will and Testament determines what happens to “your” property when you die.