Alliances, like any new player-driven feature, are a tool, that will be put to use in many different ways.
If you're a sloop looking to grind OOS, or if you're trying your hand at Athena's voyages, and you find a Galleon doing the same, you can form an Alliance, which will make the missions more difficult, but the rewards greater.
If a Galleon is going full "sink-on-sight," you can use the Alliance system to form a posse and hunt them down.
Of course, the Alliance system will be used by some to make "peaceful" servers free of the threat of PvE. While I'm not a fan of PvE servers, something tells me this will be very difficult to accomplish, at least not without a good deal of bribery.
On top of that, if the multi-crew events (such as THD) are repeated in the future, the Alliance feature will make it much easier to identify who's looking for a group to do them, rather than testing your luck by sailing up to random ships and yelling at them with the speaking trumpet.