From personal observation and experience, I believe the BR game mode got some traction after the first Hunger Games movie released. After that movie released, I remember all sorts of "Hunger Games" Minecraft maps appearing online. I downloaded, played and hosted a handful of these Hunger Games "last man standing" maps for family and friends to play.

After a few weeks of that, the game format grew stale, and I stopped playing HG maps. Then a few years later a whole bunch of BR games hit the scene and all I could think of was how similar they were to the Hunger Games Minecraft maps.

That's just my guess from personal experience.