The relatively straight-forward answer to this is that marriages produce children, and those children inherit property, claims, resources, titles, etc from both sides of the unified family. The marriage makes it so that both families in the alliance have a shared best-interest in making things work out for the same child, and therefore will work towards the same ends. A paper alliance creates no such heir, and no such motivation to work towards an end that may not be what's best for the family otherwise.

Two great examples of this, drawing on English history, present rather dramatic examples of how this worked.

Henry V, King of England, married Catherine of Valois, daughter of the King of France, to unite the claims of the English and French monarchies in to one. They had a son, born as King of both England and France. This attempt to unify claims didn't end up working out, because Catherine had a younger brother who pushed his own claim in war, and won. Incidentally, this is an example of a paper treaty failing, since Catherine was given the claim over her brother by treaty, rather than "legal right" (as it was understood). I don't want to get in to speculative history, but suffice to say there is a popular (in the right circles) line of thought that if Henry V had not died so young, or if Catherine's brother Charles had died, we might have seen a unified England and France as a result of this marriage.

The other case, where the marriage was successful in what it attempted, was that of Henry VII to Elizabeth of York, to end the War of the Roses. The Lancastrian and Yorkish factions had been warring for quite a long time over competing claims to the throne, and the marriage of the primary claim-bearer of each side ended the war by creating a unified claim in the form of their son, Henry VIII. In this case, neither Elizabeth nor her father had surviving brothers, so she was a strong enough claimant that it held. This unification is the source of the Tudor dynasty.