for the first parts yes as well as in booted applications the rate of acceleration, plus features in the ESC such as boost delay etc. All of it has to do with power delivery when you want it.

With the second thing I wrote think of a bottle full of water and the FETS being the bottle neck. The Higher constant current amperage of the MOSFETS would be like the wider bottle neck allowing more water to flow at a given time, this is what you want from a ESC when at full throttle it should pass the maximum amount of battery power with minimal loss to the motor.