Right now, there's no reason to jump into Battle Royale for anything more than the thrill of the game.
Being the only experience of its type on console, at the moment Fortnite has been able to capture the attention of millions of players thanks to its innovative gameplay, but that initial honeymoon period is going to wear off fast if Fortnite doesn't make some radical changes.
Because of how samey the experience is, there needs to be more incentives for players to keep returning to the game. Winning or placing in the top 10 currently yields nothing, and there's no real sense of victory that comes with scoring high on the leaderboard.
If the game was to reward players who won or came close to winning with cosmetic items or even loot boxes, it could offer an incentive for them to try harder. As long as they don't radically change the way the game plays, Fortnite should offer rewards that are more tangible than just bragging rights.