delarosa,
what you say is correct and this is a means of establishing the fact that the engine is producing enough power to haul the aircraft into the sky.
What is also important is the condition of the engine to produce that power and that is where the EGT (TGT) comes in.
The engine can produce the power be it EPR or N1 but at an EGT price.
The lower the EGT the less the engine is working. When engines leave the test cell they have an EGT margin. That is the EGT it takes to produce the required power and the max EGT. As the engine wears the EGT gets higher for the same power. Once you get to max EGT you have used the margin ( and the engine is removed). Especially in low cold places the engine will still make power at max egt. That's why the life on the LLP's ( see above) is rated on EGT.