It’s clearly fallacious to assume that non-profit is altruistic just because, I don’t know, for-profit is assumed as a premise to be about egotistical money hoarding.
If the reality is different, then maybe there shouldn't be non-profits anymore. In the UK for example, there are no non-profits, there are only charities. And clearly, the expectation of altruism is explicit here.
To be more explicit: Given that for-profits can be given tax-breaks for (hopefully) good reasons, what would be the reason to give non-profits tax-breaks, if not for altruism? After all, as you point out yourself, you can get tax-breaks also as a for-profit, so you don't need non-profits just for that reason.
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.