I have a theory about this. You see Elsie and Ana embrace as she comforts Ana. Elsie is looking in the direction of the now offlined Exo of Ras. And says "Ana...look". The trailer immediately shifts to the Traveler beginning it's assent. However, there is now way for Elsie to actually see that from where they are located. There were no screens online post Rasputin's disconnect, and I saw no external feeds / windows in that area. I suspect Elsie is seeing a ghost inspecting and possibly rez'ing old Red.

Because bringing Rasputin back in any way would severely diminish his ending (which was wrapped up perfectly) just like bringing Cayde back would diminish his ending.

Because rasputin was never alive. He is a machine.