Going into the business side of things again, the main deterrent in this happening for a game like Battleborn would rather be “can we afford to pay Microsoft and Sony to allow for cross-platform play for our title?”.
To break it down - the current console market structure is based around hardware sales (obviously). Sony and Microsoft make far less money on publishing their own software (which is why both companies have gradually dialed back what they themselves publish and instead relied on incentivizing developers to agree to exclusivity contracts for their platform - see: Microsoft’s recent trend of paying for a year of exclusivity on particular titles, or Sony’s exclusives on first-to-play DLC) than they do on hardware sales. For cross-platform titles this is difficult - after all, if all someone wants to do is play Call of Duty with their friends, all that matters is what their friends are playing Call of Duty on - the game is the exact same on either platform (aforementioned first-to-play deals notwithstanding). So currently, both Sony and Microsoft benefit from not allowing for cross-platform play. After all, if you bought an Xbox One and now all your friends are playing Call of Duty on their Ps4s, you’ll have to buy a Ps4 to play with them. Microsoft got their Xbox One sale, Sony gets their Ps4 sale, and both of them are happy.
So, who instead would benefit from cross-platform support from a business perspective? The publishers of course, as a wider consumer base to sell their product to means more money for them. Which means the burden of incentive would be on the developers towards Sony or Microsoft and not the other way around as it currently is. Activision would have to pay Sony and Microsoft to get them to agree to letting all that money from hardware sales to play Call of Duty fly out the window. And right now, I can list the number of publishers/developers that could afford to pony up the kind of money those companies might want on one hand. I don’t believe Gearbox would be one of them. 2K could be, but it’s likely it would only bother with it for their sports titles.
I forgot to mention a couple of factors that could tip the scales.
Paid Online Multiplayer Subscriptions. Both Sony and Microsoft utilize these on their current platforms, and this could be seen as a hidden benefit to wipe away some of the lost hardware sales - more people to play online with means more people subscribing to play along with them. I know of more than a few people who own both platforms but only pay for a subscription on the one that they have more friends to play with on.
Cross-Platform Play as a Premium Service. In the same vein as above, an easy way for both companies to make money off allowing for cross-platform play without harming their profit would be to charge for it. Something like another $20 USD added onto your yearly subscription or the like to open up cross-platform play.