Having worked for non-profit news, I can tell you that they are in effect not that different from for-profit news. The majority of their revenue comes from wealthy donors, often in the form of "major gifts". Granted, this is usually done because it becomes a tax break but that doesn't mean that certain folks with enough money don't have unsaid influence. The frequent pledge drives are somewhat of a charade in that they create the perception that they will run out of money if they don't get donations from average joes
right now. Depending on the outlet, this may or may not be the case. In big cities, non-profit media would be unlikely to go away even if most of their audience stopped donating.
In terms of journalistic ethics, non-profit is somewhat better but by design isn't necessarily free of the same crockery that occurs in for-profit news. Non-profits are more likely to get people who take journalistic ethic seriously, but non-profit orgs are also seen as career leap-pads to the big name for-profit outlets, thus you end up with a lot of the same people and similar practices that end up at places like WaPo.
I don't know what the answer is to news, but I'm pessimistic that present models of non-profit news are the solution some believe them to be.
> I wonder why [...] articles written by for-profit organizations are as trusted as they are.
That's like asking "why do people believe propaganda?" The entire business model is built on creating the perception that they are authoritative when they may be nothing but lackeys playing dress-up. Sadly, the average person receives a generally poor education and is never taught about human psychology and how programmable the human brain is, and many of the messages they've received about the world came from parents whose views were shaped by a world that didn't have the internet in its current form. You could place the truth in front of them and it's a mixed bag as to whether they take that information and form an original opinion. But if you dress that information in a suit and tie, perhaps with the right letter and color next to their name, they become conditioned to accept that information from a place of subordinance.
EDIT: I want to clarify that I don't actually like shitting on public media. There was a lot that I learned during my time in it, there are some fantastic journalists in that arena, and overall I want to be believe in the concept. I've been highly critical of just about every single organization I've ever been affiliated with, so my intent isn't to single them out.