Good point about our constitutional republic. My error.
As for all people being treated equally under the law, that would seem to say that all persons in that legal category "married" must be treated the same.
And you seem to want to open that category to any who wish to claim it.
(Which tends to make it hollow. If all of us are "special" then none of us are special.)
My point is that currently there are legal advantages to being in that category.
And as an earlier poster said, if that conveys benefits, then won't everyone want in?
And you're saying (I think) that yes, everyone should be allowed in -- no qualifying conditions.
Why don't we just save ourselves a lot of trouble, and declare every child, at birth, to be "married."