Bigger brakes give a mechanical advantage as already stated, so they will be able to work more effectively from higher speeds (in your example of locking the wheel, we will assume that the smaller brakes don't lock the wheel instantly from any speed
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). I.e. you will get more stopping power sooner and for the same pedal effort.
Bigger brakes will tend to have more rotating inertia, so actually take more effort to stop the brakes turning before they stop the wheel - you don't get this for free
BUT, what you can do with multi piece discs (like a motorbike - where the inner is forged alloy and the disc itself is a ring). Keep the inner light and make the outer part as narrow (radially) as possible.
The effective lever is through the centre of the pads, so multi caliper brakes (e.g. 6 pot calipers) can have a narrower pad (radially) but keep the same surface area, which can move the lever point away from the centre without making the outside diameter of the disc bigger. So you get the mechanical advantage without adding to the rotating mass. Obviously the decision to use 2/4/6/8pots is one of getting the right pad/disc surface area for the vehicle being stopped.
Motorbikes seem to use this far more than cars, quite possibly because they have much more to gain in keeping everything light at the front (sprung/unsprung mass ratios are poor compared to a car - also gyroscopic forces make it hard to turn a bike, so ANY reduction in rotating mass is immediately felt by the rider).
I am pretty sure that in this there are heat advantages too in that the discs/pads will run cooler.