And who in this day and age would go for either a polygamous or arranged marriage?
In the recent scandal surrounding businesses wanting to refuse gay persons there were some pranksters who ordered wedding cakes featuring a man and three women, "Happy Divorce" cakes ordered, etc., and none were (reportedly) objected to. It is interesting how "Biblical Marriage" has come to mean "almost anything but gays". While I know the issue of homosexuality, specifically, is tumultuous and difficult; the reality is first century marriage was most commonly a man of working age (late teens, early 20's, established enough to be able to provide for a family) married off to a girl who had begun her period (as young as 11 or 13). No courtship, no real engagement period; even the notion of a state sanctioned license or even a wedding ceremony. Yes wedding ceremonies did happen (Jesus was at one after all!); though they look more like what we'd call a "reception" and were largely a secular event and not one the poor often participated it. Quite literally, when you had sex, you were married. For example, when scripture uses language that Mary and Joseph were "engaged to be married" it makes clear that they were committed (likely arranged), but had not yet had sex (preserving the virgin narrative). If they were 'married', they'd have had sex. There was no such thing as being married without having sex. (In the Roman Catholic Church and in the law of many states; if you don't have sex, your marriage isn't truly 'valid'. So if neither challenges the notion that there was no consummation; the marriage can be annulled without the need for a divorce.)
Clearly marriage today is something wildly different than it once was. Even though wedding rings are blessed and a part of our liturgies in most Christian churches; that's a relatively new tradition. Engagement rings don't go any farther back than World War II. Courting was not a reality in the first century. Women, quite simply, were property to be bought and sold. You might buy your wife, or your father might buy one for you. In scripture; there are plenty of examples of wives being given as gifts. Remember the women saved from thieves and the father says, basically, "Take any one you want?". Not that fathers didn't love their daughters; surely they did, but clearly the cultural context was giving one of the daughters to the man who saved them was tantamount to if a man has his wallet stolen and someone else retrieves it, it might be appropriate to grab a bill out and give it to the good samaritan as a thank you for their good deeds. This wasn't a case of "You should meet my daughter Zipporah, you'd like her, tell you what, I'll buy you dinner". It was a case of "Here, pick one". Then you go have sex and you're married. Period.
Circuitwriter has it right that one of the issues with purity is wondering where we draw the line. Should we really be letting the state tell us who is permitted to have sex or not? To reiterate; I still think sexual commitment to ones spouse is the right thing to do. There's a lot of research, aside from the scriptural arguments, to suggest that sexual promiscuity challenges later long-term relationships. Comparisons and expectations are made. People who have few or no sexual partners prior to their spouse actually have healthier, longer marriages. BUT; it is a very valid point that the state might not be the one to decide. Like it or not; Marriage in the Church today is a service of the state with the church acting as the states officer. Some churches do 'blessings of marriages' without a license; are they 'married' if they aren't legally? Inversely, what about someone who just goes to the courthouse, there's no language about God, and there's absolutely no commitment made before God; are they just as married?
At some point we have to recognize that marriage is this incredibly complex, constantly evolving thing.
To answer the obvious question about my perspective; it comes down to commitment. If you know that your expectation is getting married legally and in the church; then I think the right thing to do is to not consider a sexual relationship with someone who you aren't committed enough with to get married. I also know people who are just as committed and 'married' but have never had a wedding or a marriage license. My own parents are that way. My mom married a very dangerous person (My biological father). He was abusive, but our fundamentalist church told her she had a duty to us kids (also victims) to 'stay married'. When she finally figured it out; she divorced him, and realized it was never for the best that she stay married. (And leading research suggests that while divorce is harmful for kids; unhealthy marriages are even more harmful). However she has been so 'soured' on the notion of marriage that the man I call my dad, who I refer to as my stepdad, is not her husband. He's also divorced, twice actually. Both times he was cheated on and left. He's a very gentle trusting guy and, unfortunately, he's been taken advantage of. He also has significantly more assets than my mom and while I don't think that's a motivation in this case, that is actually a motivation to not get married.
Personally? I'd rather see they get married. I'd rather they trust and love each other so much they'd trust each other to the point of facing an institution they've grown to distrust. However, I don't think they are "living in sin", and I don't think that God demands a license from the state in order to consider them married. I'm sure even the most hardened fundamentalist would agree that God is not bound by the actions of the state.
It's also worth mentioning that in most U.S. states, it's illegal to perform a wedding without a license (just like it's illegal to drive a car on a public road without a license). While not often enforced; a Church actually is not "free" to just have a wedding without a license. In the United Methodist Church, that's also a violation of the Book of Discipline.