Such contracts are negotiated modulo the principal agent problem. The person agreeing to the contract has incentive to make themselves look good and otherwise personally benefit, and little incentive to make it so that the organization doesn't suffer in the long rung. That the USPS has insisted on keeping this contract private is evidence of Amazon getting a special deal that would not survive scrutiny by the public or by other market participants (UPS/Fedex/DHL). In other words, corruption.

Tangentially I've heard stories of mail being purposely held back a day, to support that narrative of discontinuing Saturday delivery that was being pushed 5-10 years ago. This agency has been getting politically strangled for quite some time.