I don’t think anyone is suggesting throwing your hands in the air and making a stab at the AP engage button as an SOP whenever things get difficult.
However, in this particular accident, the aircraft is in a million pieces and everyone is dead. IF they had engaged some sort of automation, would the outcome have been different? It would be very interesting for someone with access to a sim setting it up with the published parameters (2000’, TOGA, 18degs NU, trimmed for 156kts/F15 with the speed at 180kts) and observing what happens. It might not be pleasant but will it save the aircraft, at least for long enough to give the pilots another chance?