I don't think the decision by Bezos to haul his own junk will have that much of an impact on the Big 3 provided that he takes all of it not just the easy in town stuff then expect the same discounted rate for his boonie boxes. Now if he decides to become a common carrier and haul for everybody that could hurt but I think it's a headache he doesn't want or need.
The truth is that Amazon packages move at least twice- Once when picked up, and once when delivered. You know that if Amazon is delivering packages to customers with their own ADPs, eventually they will be doing pickups too. And currently, small shippers are using the 'big three' So it isn't just final deliveries to residences that will drop. The potential is for equal drops in Ground pickups and fewer packages for line-haul. I already see lots of Amazon marked 53 foot vans going down the roads.
You can expect small shipper sends package directly to local Amazon warehouse via Amazon driver instead of fedex, then ships to end warehouse via Amazon instead of fedex, then to final customer via Amazon instead of fedex. That has to save a lot of money vs paying another company especially if Amazon can accept a lower profit on transport because they are also making a profit on the sale of the item. May only save a quarter per package, but multiply that by millions of packages, 3 million per day, and real money starts adding up for Bezos to pay alimony. Than add in another 25 cents saved on pickup and linehaul combined, and you are suddenly at a half billion per year in extra profit, with fedex losing a portion of that.