I have seen a lot of things talking about how games that cost money to buy never break into e-sports (for reasons) with a good number of them actually having their online game modes die out. Now i love this game but gearbox is going against a juggernaut known as blizzard coming out the same month as overwatch. I am not trying to compare the two it is just i doubt many people are planning to buy both these games because either can satisfy a similar itch. So i can see a lot of hurdles and trials that battleborn will have to get through before they can establish themselves as an e-sport. From what i have heard from gearbox is that they will follow the player base (i am unsure if that really is a strong commitment to try and strive out into the e-sport area to begin with) so only time will tell. To be fare i think the only reason overwatch will become anything is because blizzard will push their game into that slot and dish out tons of their own money to make it into one.
I think we focus on what in the game needs to be changed or adapted to make it an e-sport but we have to see the outside factors, such as money (from sponsors and being poured into the game by players), commitment and performance from gearbox, staying power from players, all these and more are what will determine battlebornās fate.