Who/what else is going to resolve these questions? The hospital? (Better hope the managers don't have any antiquated religious ideas.) I'm not sure what non-state-like entity would resolve disputes involving the distribution of estates or child custody disputes. What makes any of the possible alternatives so much better than a state? The reason marriage is a factor in resolving custody disputes (especially when one or both parents is not a biological parent) are obvious; because such disputes are usually highly contentious only a state or state-like entity is really equipped to resolve them.
The reason the law considers legally-sanctioned sexual relationships in these matters is that most people would want their legally-sanctioned sexual partners to have a say in them (with respect to the first three examples). (Who else would you prefer to have a say in these types of decisions by default, aside from immediate blood relatives and extraordinarily important significant others? Your room mate? Someone who claims to be your BFF?)
I'm all for expanding the social arrangements defined as "marriage" beyond two people in a sexual relationship, if necessary. But there ought to be a legal status a non-blood relative can attain that gives him/her a say, by default, in the resolution of questions like the ones I've outlined.
If you don't think the state should be involved in marriage, then fine. But the burden is on you, then, to develop a revisionist proposal that conveniently addresses how to resolve the kinds of issues I've brought up.
-WD