"Quote "Actually, the good (working) engine(s) will not be accelerated to make up for the failed engine"
Is that always the case? I have read of Automatic Power Restoration as a means of increasing RTOM on some aricraft"
Depends entirely on the aircraft, installed options/software, and SOPs of that airline.
Picking from the T7 AFM:
"When making a reduced thrust takeoff, all performance requirements
are met with reduced thrust. If desired, the operating engine may be
increased to go-around thrust to improve performance."