The USPS, when reached by CNBC, said it is looking into the issue.
At the heart of the issue is the Postal Service's essentially monopolistic hold on the letter business and whether it is using that clout to subsidize the cost of its package delivery.
To prevent an unfair advantage in letter mail, the government has tightly controlled how much USPS charges for its letters. It also instituted reforms to ensure it does not use its letter business to support its package delivery business. (In other words, use revenue from its high-margin mail business to lower the cost of its package delivery.) Doing so would give it an unfair edge over commercial carriers such as FedEx and United Parcel Service.
Those reforms, some have argued, are out of date.
The government in 2006 passed the Postal Accountability and Enhancement Act, saying the Postal Service cannot price its parcels below cost. A year later, the government clarified that 5.5 percent of the USPS' fixed costs must be allocated to packages and the like.
But mailing patterns have changed drastically over the past decade, and that 5.5 percent benchmark has become minuscule as the volume of packages that USPS delivers skyrockets.
The USPS delivered 5.7 billion packages in 2017, a 27 percent jump from 2015. It delivered 58.7 billion first class mailings, a decline of 6 percent from 2015.
"We contend that this floor for competitive (parcel) products has been maintained at artificially low levels, creating large-scale systemic economic inefficiencies engendered by what is effectively a government-enforced taxpayer subsidization of the USPS' irrational pricing," wrote analysts at Citi in April.
The package pricing, argued Citi, hurts USPS' competitors, who have to match similar pricing. It may also be hurting USPS itself.
USPS reported $69.6 billion in sales in fiscal 2017, a 2 percent drop from the year prior. It reported a loss of $2.7 billion in 2015, down from a loss of $5.6 billion a year prior.
The question thus arises as to why the mailing service appears to be undercutting itself. As letter mailing increasingly becomes a smaller piece of the business in the future, the service may not want to mess with the growth it sees in packages.
Meantime, while it could now be argued Amazon needs USPS more than the reverse, there always remains a threat Amazon could buy its own delivery service.
An earlier version of this story misstated the number of packages USPS delivered in fiscal 2017.