Salaam,
It makes sense to document a nikah and have witnesses present. The need for witnesses is by inference because in matters of divorce , when the couple want to retract, they must do so in the presence of witnesses.
The need for witnesses helps if, in the future, there is some kind of dispute, others can verify that a covenant was made.
Unlike a marriage situation, where two people are entering into a partnership, in the case of the covenants that the prophets made with God, there would be no need for witnesses at all because they are entering into a binding agreement with their Creator.
God is the ultimate witness and the prophets would never renegade on their covenants with Him because they have witnessed the truth and are staunch believers who would never deny their Lord.