I think it would be a good option to add this in. Imagine if there was a whole separate mode where you can do side missions and what not, but you may come across a small group of guardians patrolling a certain area of a map. You mad decide to sneak around them, or find a high vantage point and snipe from far away. Or even patrol around in your own group of friends killing anyone you come in contact with. The public events could be something like holding down a certain position until you or your group hits the max amount of points.
I think it would be awesome to add some world pvp. Could really change things up a bit.