Loneliness. Companionship. Fantasy. Finances. There are lot's of reasons, outside of procreation. Perhaps even more so, if there weren't little feet paddling floors and shrill laughter skippering across walls and window panes.
I accept that non-religious people have their own variety of ideas on the purpose of monogamous relationships.
People would still pair up, but the idea of marriage as we understand it would become unnecessary, since it's really there for the creation of families. I never said that kids are the only benefit of marriage - there are others, as you mention - but creating families is all that ultimately matters to the institution as a whole.
We're at the point in society at which everyone is deciding for themselves why we have marriage. Lots of confusion. It only gets annoying when people tell other people they're wrong (and even evil), when it's actually just a matter of opinion, not a matter of discrimination.