Are you saying that had the NYT reported things differently the Iraq war wouldn't have happened? That seems unreasonably strong because it implies that the New York Times had a greater responsibility for the war than did the president and congress.
The media certainly should have been more skeptical and critical of the government, but I'd say at that early stage, the blame mostly falls on Bush and his advisors. If you were working at one of these news outlets at that time, I bet you would have reported it similar to the rest of the mainstream media, too.
Even if Saddam did have WMDs, so what? So does North Korea and other hostile regimes, and so does the US. Couldn't the media have questioned whether or not that was a valid excuse for war?
That's the type of thing Phil Donahue of MSNBC did, and his questioning of the war got him fired.
https://en.m.wikipedia.org/wiki/Phil_Donahue#MSNBC_program
History is important, too, but apparently not to them. Was it ever mentioned in the mainstream media that the US itself had provided billions of dollars in military equipment and support to Saddam, including dual use technologies used for chemical and biological weapons?
https://en.m.wikipedia.org/wiki/United_States_support_for_Ir...
"You know we armed Iraq...during the Gulf War those intelligence reports would come out"--
'Iraq, incredible weapons! Incredible weapons!'
"...How do you know that?"
'Well...we looked at the receipts. But as soon as that check clears we're going in!'
-Bill Hicks