Apologies if there has been any misunderstanding: I don’t think that there is any ethical reason not to push for legalization of polyamorous relationships, merely that the social and legal complexities make it far more difficult than same-sex marriage.
That being said, I think that you have conflated any number of completely different things. For example, the statistics you quoted — 5 to 7 percent of US couples — includes anyone saying that they have any kind of agreement about extra-relationship sex. The figures of those actually practicing this type of relationship (as opposed to having an agreement of some kind) are far lower. But what do these relationships look like? What is the legal difference between a three-partner relationship and one with four? What happens to property, parental rights, etc? What happens if one partner leaves, but the other two or three want to stay together? What if they are the only biological parent of the kids, and want to take them with? What if the property is all in one partners’ name, but owned between 5 different people? All questions that would have to be written into law.
I don’t think that there is a valid moral argument against polyamory, but I suspect that you are minimizing the difficulty of the issue because you are passionate about it. In Australia at least, allowing marriage between a man and a man only requires a very small rewriting of one line of the Marriage Act. To make polyamorous marriages legal, you’d have to rewrite the entire thing. As you say, marriage between two people is incredibly complex — marriage between three is another massive level of complexity.