The combination of the technical fault and pilot errors, and modified Approach/ILS procedure per ATC instructions are at blame here. If the pilots noticed the fault and had visible & audible warnings, they should have been aware and prepared to deal with the situation without exception.
The modified ATC instructions for Approach/ILS Entry shortened the intervals and caused the pilots to be occupied with checklists & procedures at a critical phase in shooting the ILS approach as well as placed the plane out of optimum position to auto-intercept the glideslope. Normally the FADEC is slightly slow to respond to auto-commanded speed changes anyway(not instantaneous).
There's always a good share of risk by over reliance on the automation. Assumption Kills! Scans/Cross-Checks Lives! My question is, what the hell was the "Safety Pilot" doing when all this was going on? Inattention in IMC shooting an ILS is bad news.