The tax-exempt status is granted for Exempt Purposes, but not as a matter of altruistic intention: https://www.irs.gov/charities-non-profits/charitable-organiz...

For example, ask your favorite LLM search engine: Can you list non-profits/501(c)(3) that are US defense contractors?

Draper Laboratory and Energetics Technology Center are registered 501(c)(3) corporations. Their primary output is weapons research. RAND Corp, whose name you'd likely recognize, is also a DoD contractor and 501(c)(3).

The NRA Foundation and the Heritage Foundation are also registered as 501(c)(3).

Expectations are completely irrelevant. Charities steal, in the UK the largest charities are essentially run as private companies except the shareholders are employees. Same thing with government, there was a unit of the government that spun out to a "non-profit" structure, some of the civil servants ended up becoming shareholders, and they now lobby their friends in the civil service to use their services...afaik, the government is still their only major customer and they were at, for example, all the pandemic meetings. Just generally, the UK has a vast network of these organizations that have a significant role in government policy but are totally outside the government (this is also true, actually even more so, in devolved countries...to a large extent, government policy there is formed by unelected private institutions).

There are no real rules here beyond humans act self-interestedly. No structure will contain this. This happens in for-profit companies with shareholders too. Principal-agent problem.