4 player splitscreen was kinda a marketing gimmick i think.
Borderlands was build with more performance restrictions, so it could run on a Xbox 360 for example.
Xbox One is +/- 8 times the power of a Xbox 360.
So $ player splitscreen was something fun they could do. It made sense for the franchise, but it also creates a unique selling point so it would get some buzz / headers on (game)sites.
Randy Pitchford stated that Battleborn has ‘4 times’ the fidelity as Borderlands, so that asks more performance from the consoles. Draining resources for 4 player but it’s capable to do 2 player splitscreen (but at what costs, maybe frame rate, maybe lighting/shaders).
But then i ask you @Jax_Rift why have 4 player splitscreen if you have 5 player modes?
Are you also asking for a companion app so it can run Battleborn on a tabled creating a fived player! 
