Having said all of that I am still fine with the concept of “marriage” … as I conceive it. Historically “marriage” has meant different things, as you pointed out – I would not, personally, participate in a “marriage” that implied “ownership”, for instance. Lucky for me, I live in an age and a country where that kind of arrangement can not be forced on me. (I'm agnostic/atheist so I'm not terribly interested in what various churches say on the subject).
Marriage, to me, means that someone has actively decided to commit themselves to facing life as a team with another person(/other people)...and to announce that intention publicly. It doesn't take a church or a government to make that promise “real” … just recognized. The ceremony is a physical act that you take part in to mark the transition., the “piece of paper” is just a “piece of paper” … except that it is a symbol of what has occurred.
Liken this, perhaps, to education – say you take all of the classes you actually need but never actually complete the requirements for your degree – you never took that gym class. You still know what you know, you are qualified for the jobs you are qualified for but you don't have that “piece of paper” - should that matter? No. Does it?...more times than it should. Do you need to go through the “cap-and-gown” ceremony to get that piece of paper? Nope. So why do so many people do it?
From my own experience – getting married meant something to me personally. It was fairly subtle. My thought processes went from “I am going to do this-and-such...and MrS will be there too.” to “We are going to do such-and-so-on.” Our actual plans did not change. Nothing changed on an observable level. We lived the same life we had been living before.
I don't think that marriage has to have anything to do with sex or the ability to procreate. For, me marriage is about making a commitment to being together and forging a life together...and, lucky for me, nobody but me and my spouse has to agree.