I can't help but wonder why they need to be involved at all.
The one that springs to mind immediately is the inability of a court to force a spouse to testify against the other. Obviously, no legal agreements between the two of you can prevent this.
Second, joint tax filings. This is really important, because getting married does change your financial status. If the government doesn't recognize you're partnered, it would treat all stay-at-home moms as if they were essentially homeless, without income, etc.
Third, social security, medicare, and disability benefits can be given to spouses automatically after the death of one. If the government didn't recognize their union, the surviving spouse would have no claim to these, because they couldn't enter into a legal agreement which would force the government's hand.
Fourth, the ability to enter contracts for the other party. You can do this to a certain extent with a power of attorney, but it's really not the same. Let's assume, for example, that we're living together and not married, because the state doesn't recognize it. You die. Can I automatically renew the lease, if you're the one who signed for it?
Fifth, let's take my publicly funded school for an example. My health insurance covers spouses, but if this was not recognized by the state... how does the state know whom to cover? Educational benefits, etc. fall under this difficulty as well.
Sixth, suing on behalf of your spouse. Let's assume you're in an accident because the other guy was drunk and I want him to pay for your medical bills. I don't have any legal claim on him, however, because I'm just a bystander, as related to you as the hotdog vendor who also witnessed the crash. And let's say we do successfully sue - I can't receive the money.
Seventh, marriages can no longer be used to support citizenships. So, I flew over to Russia and fell in genuine love with Svetlana. The government doesn't recognize a family and, even though she's much more solidly based in the USA than most single immigrants, might not ever be able to come over.
Finally, and this has happened to me personally, visitation to hospitals and jails is restricted to family members. If, say, a Catholic hospital chooses to turn you away because you're not legally married, you have no legal recourse if the government does not recognize a union.
Etc., etc.
Merging assets? End of life issues? Property ownership? You can do all of those things without being married. You can get a mortgage or a lease with anyone. You can merge assets with anyone. You can write whatever you want in your will. What if you just had to fill out more paperwork?
Because gay marriages are illegal in my state, I had to do a lot of this. It was relatively expensive and we still don't have all the reasonable rights which
automatically come along with marriage. Furthermore, we can't put ourselves into an agreement which the state would ever recognize.