To answer the OP: Why shouldn’t they?
In the semi-recent past, a particular progressive Democrat was accused of nefarious things by the right-leaning media. To the extent that these allegations were mentioned in the left-leaning media, they simply said, “There’s no evidence to support these allegations”. I looked at the allegations, double-checked that the evidence which had been provided proved true and to the extent that I was able to do so, everything that had been said was independently verifiable.
Later, one left-leaning source did a follow-up article where they stated what their methodology was for ascertaining that everything was a lie created by a troll. That methodology was to perform a 5 second Google search and look at the page titles in the search results. All of those search results were angry progressives posting about the topic, from after the incident in question, calling the accuser a liar and troll. I changed the search range to exclude anything after the incident and read posts by and about the accuser and they seemed to be a respected, reasonable person.
Fast-forwarding to the impeachment of Donald Trump, the one thing that I called for the House managers to do was to build a full case against the man. I believed that they needed to start from the beginning and establish that Trump was a crook and conman and that it was reasonable and correct to assume, based on his past and basic character, that everyone’s assumption that he had nefarious intent in his activities with Ukraine should be taken as fair and reasonable.
I’ve read enough about him to know that such a read is correct and that the assumptions made by everyone - Volkman, etc. - were just the obvious. But your average person reads the news and they never see any big attempt to prove anything, just to assert it, and it’s not difficult to find examples where those assertions are clearly specious.
I mean, if I say that “there’s no evidence” well…how did I determine that? Did I do a six second Google search? Did I go and sit in a dark closet for 5 minutes and shout, “No no no!” while covering my ears? Or did I go talk to all the interested parties, a few insiders, experts, etc.? Only one of those is authoritative in any way but from “there’s no evidence” it’s impossible for me, the reader, to ascertain what was actually done before the person came to that conclusion.
Reasonable people who read most media sources realize that those sources have some a priori assumptions that guide them. You don’t need to prove that Trump is a conman. It’s already “known”. You don’t need to defend a progressive Democrat, their innocence is implicit.
And, the important thing in all of this, is that there’s no media source which says how they reached their conclusions. They never state their methodology. They rarely go back to cite older articles and, often, when they do the older articles don’t really match what the new article says it said.
Basically, Middle America reads their media and buys into it because they have no reason to buy into anything else. Likewise, Coastal America reads their media and buys into it because they have no reason to buy into anything else. It’s all surface layer only, whichever group you happen to be a part of. And both sides are largely just taking free material (when it comes to politics) from politicians and running with it, as a lazy way to make content day-to-day.
To get Middle America, the left-leaning media would need to present their work and that would mean, for one, to go back to the beginning and prove their a priori assumptions.
They should.
They won’t. If Adam Schiff can’t be talked into running Trump into the ground, in a reasonable and professional fashion, I hold no hope that the New York Times will.