The probes and ports for measuring these pressures can easily become contaminated by bird remains so sending incorrect information to the fuel scheduling systems.
The esteemed Mr. Farley makes an excellent point, although I think the only sensor actually in the CFM56 flowpath is the T25 temperature (between the low & high compressors), and the FADEC is undoubtedly programmed with a fail-safe schedule to permit partial power recovery if T25 is lost.
The significant damage in this case is likely in the HP compressor airfoils - bent, twisted, broken, "corncobbed" in airline slang. They were simply unable to pump any significant airflow through the burner and turbines - and it's airflow that makes it go.
A modern high-bypass engine's core is smaller than older donks, and it's coupled to a bigger fan. This means two things:
1) the inlet area of the core is smaller, so it's a smaller target for a bird to attack
2) if a bird successfully attacks the core, it does proportionately more damage!
