The fact that the best way to play and do well competitively in fortnite is to run away and avoid all interaction is a problem in my opinion. Here's the key, the GAME needs to reward aggression NOT the competitive formats.
How about if you kill someone, they only drop their inventory items, and instead you get awarded a set amount of resources (ammo/mats), maybe as Poach suggested, these rewards are different depending on the current game state (# of circle, # of people alive or something)