The question is: if the EEC operates in ALTN mode, why does the N1 become RED if I put the throttles full forward? Doesn't the EEC protect against overspeed in both normal and alternates modes?
If I understand correctly you are mixing 2 limitations. N1 and N2 redline overspeed protection is a protection against structural limits (how fast can my rotor rotate?). It does not verify max EGT which is also a fixed limitation of the engine.
In normal mode, EEC calculates the N1 limit that is associated with the approved thrust limit (full rated or derated). This is a different N1, and the value depends on ambient conditions. Different ambient temp and/or pressure give a different N1 value indicating the related rating. This is important as the engines are regulated using N1 (unlike EPR ie) so the EEC continuously updates this N1 reference. When the EEC switches to soft or hard alternate mode, this realtime calculation is lost and hence the N1 is not automatically adapted. So you might end up boosting the engine, but the calculated N1 limit might be wrong as well. Note that the parameter to regulate the engine is N1, only N1.
The EEC will never allow you to push beyond the structural N1 AND N2 limit (but not EGT).