1. Reporters and editors cannot possibly be aware of their own bias because they have their own world view, through which they perceive their own reality.
2. Because reporters and their editors cannot be aware of their own biases, fundamentally all news is biased, intentionally or unintentionally.
Your argument depends upon #1 to be True. However, people can know their biases and adjust for it. But at the NYT, editors and reporters are aware of their internal biases, so #1 is actually False.
So then #2 leads to something like #3:
3. Fox News, while intentionally biased, provides balance to the obvious left leaning bias of the NYT because of #1 and #2 -- even if they don't fully vet their stories [1].
So personally I would prefer to get my news from people that research and report facts. Facts, in and of themselves, are unbiased.
[1]: https://en.wikipedia.org/wiki/Murder_of_Seth_Rich#Fox_News_r...
Here's a snippet of the public apology the NYT published after the 2016 election. Maybe with honesty, or without fear or favor means something different to you than it means to me.
https://www.nytimes.com/2016/11/13/us/elections/to-our-reade...
>As we reflect on the momentous result, and the months of reporting and polling that preceded it, we aim to rededicate ourselves to the fundamental mission of Times journalism. That is to report America and the world honestly, without fear or favor, striving always to understand and reflect all political perspectives and life experiences in the stories that we bring to you. It is also to hold power to account, impartially and unflinchingly. You can rely on The New York Times to bring the same fairness, the same level of scrutiny, the same independence to our coverage of the new president and his team.