Reduced Thrust using ATM results in a longer take off run. The conditions under which the restrictions apply have increased risk whilst on the ground. Thus, the use of full thrust gets the aircraft off the ground quicker, reducing the risk, but not necessarily to the normal, non-restricted value.
Brake deactivated or anti-skid INOP in case of an Rejected Take Off.
Takeoff runway is contaminated RTO considerations and slush drag during takeoff, or low friction / crosswind control.
De-ice fluid applied potential drag increment, reduced lift and/or trim (rotation) issues aircraft type dependant.
LVO takeoff questionable, but it is better not to be on the runway if you cant see objects.
Reduced thrust (ATM) is not the same as derate
see previous thread post #5.
Derate is a fixed thrust value, but less than the engine is certificated to produce. It is the agreed maximum thrust for the engine installation/use. The AFM aircraft handling limitations, Vmcg etc are based on this value. Therefore any higher value of thrust cannot be used (there may be specific exceptions).
With reduced thrust, the thrust level may be restored to the full value (but not greater than the derate value if applicable to your type).
Takeoff performance and aircraft handling considerations do not require any thrust increase in the event of an engine failure.
If your aircraft uses derated engines and reduced thrust is an approved operation then I assume that the restrictions also apply.