It's not enough for the two people to trust each other because they have parents friends etc. These people, and societies norms are a huge influence on the decision to get married.

But I do think at the end it all boils down to trust. If marriege was not an external event, then why the ceremony? The rings? Etc? It's full of symbolism describing and alluding to your responsibilities and how you're going to be judged for not abiding to them.

So yes, in a world where two people have total trust, and society is more lenient in it's pressuring of norms marriege would be obsolete.