Wow. Someone doesn't appreciate just what legal benefits a marriage grants. Let me start with the big ones:
1: Presumption of paternity. I'm married, and my daughter is sitting beside me. I do NOT need to do anything to prove that she is my daughter, and should it ever come up (like, say, if my wife decided to leave me after becoming pregnant) the burden of proof is on whomever is saying my child is not mine.
2: Tax benefits. In addition to being able to pool income for income tax purposes (which would be much more significant if we didn't both work), we also jointly own all marital property. Which means when one of us passes away, the other one doesn't "inherit" anything -- and so, even if we owned billions of dollars, there would be no inheritance tax. It also means we can give each other money without having to have the other one potentially report it as gift income. (Yes, the benefit is fairly mediocre for most folks. But if you're an edge case, it can be a lot.)
3: Legal protection. The only person who is absolutely prohibited from testifying against you in court is your spouse. (Ok, not "absolutely", but provided it's not a domestic crime, it's pretty high. Higher than lawyers or doctors or priests.)
4: Automatic visitation / power of attorney. When one of us goes into the hospital, not only can the other one automatically visit, but we also automatically get a limited power of attorney for medical decisions as the next of kin.
5: Inheritance rights. She can't write me out of her will, and I cannot write her out of mine. (see #2, above. And yes, it does matter in several cases.)
So, those are the benefits that a polygamist (or a polyandrist, or a polymorist) gains. But multiple concurrent marriages aren't illegal because they somehow grant too many benefits; they're illegal because they stress the dating pool. If we adopted bigamy, for example, we'd have ~25% of the population that simply cannot find a wife, because they're all taken. And that 25% of the population might just stay home and play video games -- or they might go out and take wives wherever they can be found, including acts as vile as rape and murder among the instances which would increase.
(And, yes, a gender-neutral multiple marriage law would make sense. But it also makes sense to just ban them altogether.)