As I pilot, I'm with you. Attitude + power = performance. Simple, but...
... I think it's a bit more complicated than that.
At the altitudes they fly at there's probably a lot less margin between stall and Vne or Mcr or whatever limiting speed they have that makes hand-flying tricky, especially with a non-functioning pitot-static system.
In hindsight yeah, they probably could have saved it but in the heat of the moment...
First they'd have to identify the problem as something dangerous, not just a computer throwing a fit due to a bad sensor. You don't just give full power and put the nose down on an airliner at ~30k ft cruising around 0.8 Mach with no visible horizon.
Once the problem is identified as real they'd have to figure out what the problem really was, which instruments are lying to them and which can they trust. Determining that the issue was a problem with the pitot-static system, not with some other system isn't that easy at night at ~30k ft with no reference to anything other than their instruments. Their given a bunch of data and have to use that data to figure out the issue, it's more like working out an algebra problem not figuring out a mechanical problem (obviously I don't know to what extent their emergency checklists and computerization would have been at this). It's not the same as flying along at 3000 ft and noticing your airspeed indicator isn't matching the feel of the controls, the speed of the ground going by and the sound of the wind rushing past and going "Huh, my ASI might be broken, better keep a bit of extra speed on final for safety... I wonder how much that's gonna cost me to fix"
Once they've figured out the problem they'd have to figure out what to do about it, how to get control back and keep control using whatever instruments do work.
"An accident investigation hearing is conducted by non-flying experts who need six months to itemize all the mistakes made by a crew in the six minutes it has to do anything."