According to [url=https://www.youtube.com/watch?v=47RMUsen3c0&feature=youtu.be]this interview,[/url] Bungie's own original plans to have pets in Destiny, and it was reflected in the concept art attached to this post, but the idea later morphed into the ghosts we have now. I think ghosts make more sense because flesh-and-blood animals could not survive the dangers we encounter. That said, I think there is still a sensible way to kind of have both.
Ghosts are made of the Traveler's Light, and we know Light can be remolded into different shapes like Sunbreaker hammers and Nightstalker bows. Given this, the Ghosts could take on different forms resembling pets made of glowing Light. [b]These new shapes could be accessed through special cosmetic ghost shells in Destiny 2. [/b]
Such forms could include white tigers (like in Bungie's concept art), serpents, Vex harpies, weird inanimate objects, or whatever strange things the concept artists could think of.
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Well, it's clear that it's not going to happen. If it would happen, I would love a peacock shell for my ghost: http://images.hellogiggles.com/uploads/2017/03/23035640/GettyImages-656739704.jpg