Given the meteorological conditions at the time of the near miss (mainly very low visibility, low ceiling) and the lack of ground radar, I think we all agree that ATC should not have cleared the WN flight for takeoff. Some folks have mentioned the WN pilots, but why did they accept the takeoff clearance? They knew (well, they were advised of this during the takeoff clearance) there was a FX heavy on three-mile final and there wasn't much of delay that could be made from the clearance to getting the aircraft going on its takeoff roll. From the preliminary report timeline, it appears that roughly a minute and a half passed between the takeoff clearance and the beginning of the takeoff roll. That's a significant amount of time given that an aircraft was on a three-mile final. From the report, the WN pilots seem to indicate there was no delay. Basically, they accepted the clearance, taxied onto the runway, lined up the aircraft, the captain gave control to the FO, and the takeoff roll began. I'm sure there was a lot more questions and answers during the interview, but that's all that's been released so far. But there *was* a delay, some of that possibly being attributed to what others have alluded to as a 20-30 second engine run-up for engine anti-icing.
It's possible that due to an intense workload, possible issues in the cockpit that needed to be addressed/resolved, very low visibility, etc, both pilots just flat out missed (or didn't process) the part of the clearance that mentioned an aircraft on short final. Surely the NTSB asked them if they heard that portion of communication and if the pilots answered 'yes' then the next question was why the accepted the clearance but yet took 1.5 minutes to begin the takeoff role?