Marriage is but a set of constraints designed to make two people cooperate to achieve a win-win scenario; If the two people actually trusted each other, they wouldn’t marry.
In particular I find a lot of people Think of "marriage" as an external event driven thing - a ceremony, a signing, the guests, potentially the name change, and of course the laws and such.
Anyhoo, Do you essentially propose that no two people who trust each other would marry, and if so, why?
It feels like such a strongly universal statement that it cannot possible hold true...
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.