By the same token, ignoring the objectives of the arena will also cause a loss. For example, if you let the other team get all the big ice, or don’t guard the tomeliths you take (which add to your score as long as they’re in your team’s possession), etc.

That’s one of the things I actually enjoy about pvp in FFXIV, is that it’s not just mindless pvp. Knockouts and battle high are important yes, but the arena objectives still need to be met. The winning teams are usually doing a good balance of both.