Now I understand your definition of "ideal transmission"

So your "Ideal transmission" only provides a finite
number of gear ratio selection.

In this case, horsepower curve is very important.

For any engine with a sharp ^ horsepower shape and given a transmission.

We can always find a engine with a little lower peak power and different power curve, match it with the
same transmission, then we can beat the other engine in
certain situations.

This is because, ideally, you want your engine work
at the peak horsepower point. But because the transmission only provides finite number of gear ratio,
sometimes you have to let the engine run at the range
far away from peak power point.

For example, at the low speed, say 0-20mph, most vehicles have to run at first gear. Because of this,
the engien has to run at rpm way from peak power point.
If the engine horsepower shape is linear than X*X shape, it will get accelerated faster.