It irks me that you missed an important distinction
The question conflates private consensual agreements between adults and state marriage as a bundle of legal privileges
If three or four adults want to live together, fuck each other, pool property together, or sign private agreements, then what exactly is the rights-violation that would justify prohibition? I'm not seeing any, and nobody identified one. Abusive sects, rape, demographic agendas, or the brainwashing of girls are separate violations that would still be violations in a monogamous context. Coercion, grooming, fraud, captivity, those are violations that ought to be prohibited. But the number of adult partners involved does not by itself create those violations. If the concern is child welfare, then please identify the specific abuse, neglect, abandonment, or coercive dependency that is inherent to non-monogamous family structures and address that directly.
Now, whether plural relationships are wise, stable, or culturally desirable, those are different questions from whether they should be illegal. That is, just because you don't like something does not automatically justify banning it.
If the real point is narrower, i.e. "state marriage law was built around a two-person template and gets messy with inheritance, taxes, custody, testimony, immigration, and divorce", alright. In that case, the argument is not "polygamy should be illegal", but rather that a state-designed legal package becomes cumbersome when it's expanded beyond the shape it was designed for. Which would be a limitation of the state's marriage machinery and not a proof that peaceful plural unions are illegitimate.
The premise that the state gets to decide which intimate arrangements are legal or illegal in the first place is doing more work than any anti-polygamy argument in this thread.