> Why is it that multiple delivery companies are able to survive on their own in the free market, yet the USPS cannot?

USPS operates with many government mandates that don't apply to private companies.

Some of the financial woes are actually inflicted by the government. For example, the government mandated that the USPS pre-fund retiree health benefits well into the future, in a way that no rational private company would ever consider. This alone has contributed significantly to their cash flow problems:

They even provide a convenient chart of how their profit/loss looks without the pre-funding requirement, at least up through 2010: https://about.usps.com/who-we-are/financials/annual-reports/...