If they can't do it better/cheaper then the reason to do it is because UPS or Fedex are rent-seeking, and doing it themselves would bring Amazon's cost close to the actual cost of delivering
Amazon Fresh (groceries, which UPS/Fedex cannot do)
1 hour delivery (which UPS/Fedex cannot do without keeping their fleet at Amazon's warehouses)
Restaurant delivery
etc
The point is to capture the means of delivery so they can become the carrier for parcels/food/whatever. Uber is trying to do this too. As is Postmates. UPS/Fedex have the issue that they are very good for bulk travel, but weak at last mile (it works for them now because of the volume they do, but the best they can reasonably do is next-day).
Amazon only has to move things between their warehouses and consumers. 99% of pickups are at their warehouses. Hell if they use UPS/FedEx for returns then it's 100%.
One word: Teamsters.
UPS drivers are Teamsters. Which means they have good paying jobs with pensions and fringe benefits.
All Amazon has to do to be cheaper is to hire no-benefit minimum wage part-timers. Or even better, just use independent contractors. It's the Uberization of package delivery!
It will be far cheaper, but it won't be better.
Fedex never really got Fedex Ground right.
And don't get me started on why they have to use 16 digit package tracking numbers that start with '1Z'. WTF?
Amazon is looking at hitting the low hanging fruit first. Where they can ship large amounts of times from point A to point B then have USPS or their own carriers deliver. They're not trying to compete with UPS or FedEx today. Maybe some day in the future but that's years off at best.
If they can do their own shipping for certain items to certain locations (especially if they need to move an item to another state before having UPS / FedEx / USPS ship it) they can likely save some money.