My educated guess, good enough for a real solid rumor around the belts...
Think something like Ground 60-65% and Air 75-85%.
So think of a $10 list ground package (something smallish) your typical solid customer would be paying around $7.50, Amazon will be paying around $4. Now do you think you make enough profit per package to eat that $3.50 difference? Well your quarterlies do not state that kind of profit per shipment on avg.
That is where large metrics begin to factor in, you hear things like "Pays for over-head", from my travels, some of that is true, but it is also usually gray trying to be precise with a lot of numbers factored in.
Would you do better not having them and cutting over-head (jobs/machines) accordingly? Perhaps. Or will your profit per package take a hit on the rest of your remaining volume? Perhaps.
It seems like Wall Street likes growth, so lets say you had a better bottom line, but your volume were down, they worry about that. What they want is both, better bottom line with growth showing. Most likely some of the leverage an Amazon sized account would have and yes... they'll know that.
Does UPS or Fedex survive without Amazon, of course. But it may cost some jobs. Another educated guess is USPS is seeing Amazon growth. Why? Cheaper yet. No dim rules. Sunday and Sat for nothing. Still deliver adequately no matter what a rival driver may think.