The real problem is that government has gotten into the marriage business and it doesn't belong there. The issues you mentioned (child custody, hospital visitation, inheritance rights) really have nothing to do with marriage and should all be assignable without a government endorsed marital contract.
Meanwhile, my/our camp of libertarians saying hey, the Government really shouldn't be in the business of deciding who can be in what sort of relationship with who else or blessing either side of a controversial argument is disappointingly small and quiet and usually ignored.
On the other hand, we have people being harmed by the unreasonable jank thrown at homosexuals who wish to marry. The perfect must not be made the enemy of the good out of a sense of ideological purity.
The thing about Government power, though - everything seems all nice and cool when it's pointed in a direction that you like, and it makes everything happen real fast and lays the smack down on your ideological opponents. But that power can turn on a dime and get pointed right back at your side, as has happened a great many times in history. Think it can't happen here? I hope it never does, but it does have a nasty tendency to happen in places and to people where they thought it couldn't, where they keep on doing the simple and efficient thing, because that couldn't possibly ever happen to us, right?
Politics is the art of the possible: extending marriage benefits to gays and lesbians is a lot easier than clawing it away from all straight couples in order to satisfy a desire for libertarian ideological BS.
But then, this was never really about benefits in the first place. If it was, they could have had civil unions a decade ago. This is about getting the Government to endorse it as Marriage to stuff it in the face of all the homophobes out there. This has always been entirely about ideological "BS", but not the kind the myself and any other libertarians are spewing.
And stuffing a few homophobes is good. They have been persecuting LGBT people for millennia so fair turnabout.
Smart folks have said that the reason homosexual marriage even became a thought was because of the transformation of marriage from a bond of ownership of man over woman to a shared partnership. A polygamous arrangement (as per the mormon church, not the polyamorous relationships of the hippies, etc) ends up with a hierarchy of power with one man controlling multiple wives, with the power to divorce, ruin, etc the others if they don't allow him to wed again.
I think an argument for polyamorous marriage could be made, but polygamy is essentially a raw deal for whoever isn't the hub of the marriage wheel (one man in the case of traditional mormonism, islam, etc.).
Quite literally, I imagine it would go something like:
Do you take this woman to be your wife? I do.
Do you take this woman to be your husband's second wife? I do.
Do you take this man and woman to be your husband and second wife? I do.
That's how three adults could all consent.
You can argue that someone is being forced to say yes, but you could argue that in any type of marriage or contract.
That said all of the legal agreements become far more complicated and likely null and void if one person drops out or is added. I think an argument could be made, but with the complication you're basically saying polymarriages would be like corporations, with their associated complexity.
Polygamy as practiced now is a "bring more childbearing women" into the flock type thing, which is by nature non-equitable. I doubt most folks in a polygamous marriage (by choice) would want to get involved in a polyamorous marriage and as such, I think you can't legally support a non-equal union of that sort.
Hmmm, please excuse my ignorance in such matters. I only married one woman and that is quite enough.
>you're basically saying polymarriages would be like corporations
Yes, exactly. Well put.
>with their associated complexity
I can't even begin to imagine the complexity, legal or relational. However, I can imagine situations where such an arrangement could be beneficial to the individuals involved.
Are you trying to say multiple adults can't all agree on something? Your argument is based on ignorance and you're no better than the people who oppose gay marriage. You've been fed Christian and feminist propaganda to make you believe that only two consenting adults can love each other and that if you happen to love more than one person you shouldn't have the same rights as other people who don't.
You basically don't think polygamists are equal. Now let's see you do a full 360 from being pro-equality to using the same arguments the bigots used against you.
EDIT: added source; had previously assumed this was common knowledge
Scroll down to section 3.a.ii (or ctrl+f search for "Implication: monogamous marriage reduces the spousal age gap, gender inequality and fertility")
Anecdotally, this is what a family friend who worked as a counselor for Southern Utah University observed repeatedly. SUU is located in Cedar City, which has one of the highest concentrations of present-day polygamists in the US.
For one thing, looking for younger women / men is not wrong. As long as they're consenting, and old enough to consent.
Further, any relationship of any kind has the potential to be abusive. This is no ground to say it shouldn't be allowed. This is like the idiotic christian bigots that think homosexuals are bad because they're child molesters. No, they're not.