After reading multiple reports, I am confused if anyone really knows if it is profitable or not. Do you have a source for your claim ?
UPS and Fedex have operating margin of ~6%. They have spent 10's of billions of dollars into optimized sorting facilities and logistics. Yet, Amazon uses USPS for last mile delivery. USPS also has to deliver to non-profitable remote locations and has public unions which demand above-market salary/pensions. A less-optimized player with higher cost base offers service at lower cost than a business with 6% operating margin - simple math makes me believe they are losing money on those orders.