Amazon is a very forward thinking company. If I were a betting man, I'd place my money on Bezos.
Look at the stock chart for purple right after that Morgan Stanley report came out. You'll notice it nosedived (and UPS to some extent). Wall Street knows where this is heading. Brown and Purple's CEOs can knock the research all they want by stating how large their network is and how insignificant Amazon's business is (for now) compared to the big picture. The reality is they are both feverishly working on their own drone delivery programs and how to control labor costs in the future.
The elephant in the room is artificial intelligence and it's coming to a theater near you. It sounds like science fiction now but it's being developed rapidly. While pilotless aircraft are probably a little ways off, I think you'll see it first in cargo. At the very least, you'll see single pilot operations. Passenger aircraft will likely take longer to adapt until XYZ Drone Airline forms and sells tickets at half the cost due to reduced labor costs. The general public already thinks "planes fly themselves".
If you are interested in this kind of thing, search for Jack Ma (Alibaba) and AI. His point is that technology is not linear. Once this technology is developed it will rapidly take over industries (not just aviation).
IMHO (and gazing deeply into my crystal ball), I don't think pilots have anything to be worried about at least for the next decade or two. But if I were looking at a 40+ year career ahead of me I'd definitely be concerned. It wasn't too long ago when there were five people in the cockpit and now there's two. I don't think a single pilot airliner is too far fetched and would solve the "pilot shortage" issue rather quickly.