Show me where you derive higher "total friction" in relation to "total swept area"? If we have 20-lb of force from each caliper arm, how does that affect how much friction we have on the pad? If we upgrade to a pad twice as large, do we suddenly have twice the friction? Why bother with brake-caliper designs and upgrades at all then? Let's just slap bigger pads the size of bananas on and that's all we need.

The reason we don't have pin-head pads is that in order to generate that same amount of friction on a smaller surface area, you'd end up wearing away the pads in a single stop. Again, review f=mu and you can even calculate deceleration-rates and stopping-distances if you want. The limiting factor in the end is the maximum amount of friction the tyres can generate against the ground.

Also, race-car brake-upgrades is to shed heat. Dissipating 3000lbs of kinetic energy into heat is what slows down a car. Bigger, heavier brake-rotors heat up less for the same amount of heat generated (they're heatsinks). Their larger surface area also sheds heat faster. This allows you to not overheat the brakes on the track and can do repeated stops over and over again. Big brakes will last 100-laps while small ones will overheat and boil the fluid, resulting in fade within 10. But any single stop (starting at the same brake-temperatures), with bigger brakes will not be of shorter distance or faster than smaller brakes. It's durability we're after. The only way to significantly affect the braking-distance on a car is to get stickier tyres, lower-weight and/or increase downforce.

The diameter of bike-brakes don't change, so we can't compare with auto brakes. What larger diameter rotors do is allow for more mechanical leverage against the tire. Imagine two levers, the pivot is the hub. One lever is with the contact patch on the ground to the hub. The other lever is from the middle of the brake-pad to the hub. Since the diameter of the rotor is smaller than the tyre, the resisting torque generated by the pads is smaller by the time it gets out to the tyre. What the larger diameter lets you do is get more resisting torque on the tyre with the same pedal-effort or pad-force. In the end, braking distances will still be determined by total friction of the tyres on the ground. Just that with larger rotors, you can lock them up with less pedal-force than with smaller rotors. However, braking-distances will still be the same. It's like grabbing your brake-levers at the tip or in the middle. It will require less finger force at the ends of the lever for the same braking-force as squeezing in the middle... however, your braking-distances will still be the same.

With bikes, the diameter of the braking surface is always pretty close to the diameter of the tyre. If you want to compare disc brakes vs. calipers, you'll find that you have to apply a LOT more force at the disc in order to generate the same braking-power as pads on the rim.

BTW - I did a test of maximum-braking that San Rensho mentioned. Came up to a stoplight in the bike-path next to the cars waiting. Picked it up to 20mph to have a standard control speed, slammed on the brakes as I passed the rear-bumper of the 2nd to last car. Let go of the rear-brake when my seat came up and hit my belly and I was pretty much fully stopped by the door of the 1st car... Eased up on the brakes to reach the crosswalk in front and grabbed teh front-brake again and hopped/pulled up on the pedals. Held a nice stoppie for about 2-seconds...heh, heh...