I think that giving more recent examples would strengthen your argument.
There has been no incident as bad as the reporting that lead to the war in Iraq because the US had recognized that entering the war was a huge mistake and became somewhat resistant to the type of propaganda that lead to it.
It does not matter if the nyt is usually factful. If they can be subverted by powerful interests to push an agenda, they are not trustworthy.
OP also contains: "Investigating facts and reporting them clearly is a solved problem."
NYT remains one of the more reliably correct news sources in the US but they all make mistakes - sometimes accidentally sometimes maliciously. Since there are humans involved you need to understand the biases the news sources have and compensate for that yourself.
But shouldn't we not continue to consume sources that have made malicious mistakes? Even if the maliciousness was a bad outside actor feeding incorrect information to ethical reporters, isn't it likely that such a source will make a malicious mistake again? When the consequences are on the scale of directing the country into a fraudulent war, how can we ever trust their reporting on anything of consequence again?
I can't really answer what the best tactic for weighing news sources is since I think that the true measure would need to involve observing the reporters and editors behind each specific article which isn't really feasible. I don't think it's wrong for you to be hesitant about trusting NYT, and feel free to never trust an article written by Miller - I personally think she's shown a lack of care for discovering the truth - but... Eh, balance in all things.
I think a browser extension that alerted you when an article you read was corrected would be interesting.
And if they later investigated themselves and found that they published information that was not true, would that cancel the war pushed on us by the military industrial complex across all of our media and bring 500,000 dead Iraqis back to life?