There are lots of implications for contemporary situations. 

Since Catholics have always believed and taught (but rarely discuss) the truth that couples marry each other and that the real sacramental action happens directly between the hearts of the betrothed couple, and not on account of anything the priest "confers" on them, I'd say there are many ways the ancient Jewish ritual you describe could be used to remind us of our common roots as it relates to the sacrament of marriage. In fact, I'd go further and say that if we really believe that, why should any church authority ever dare to question the marital legitimacy of gay couples who believe in their heart of hearts that they have already married each other? 

Then there's the lengthy history of couples living in remote rural areas who marry themselves only to have a priest bless their marriage after the fact, or the slaves who "married" each other by jumping over a broom without the benefit of the church or the state's blessing.