TBH, if any FPS franchise could actually present a solid Battle Royale mode... it's this one!
Massive Maps and player count = A cornerstone of the franchise
Vehicles = Have your pick
Gun-play depth = Miles ahead of the other popular titles
Parachutes = Just pull the cord
Add in artillery barrages or gas attacks to simulate the safe zone, and they'd have the best Battle Royale mode on the market...
I guess we'll just have to settle for the normal BF experience: random public lobbies with ridiculously skilled team hogging the best vehicle (which no one can kill) and the endless cycle of spawn kiling.