So are you agreeing or disagreeing with my quote?
I'm presuming your bike brake is a hydraulic disc brake? which is just a miniature car brake and pretty much works the same (except no engine vacuum assist). If you've used a braided hose instead of a normal flexi pipe you'll have a firmer lever, same as a car.. the only difference is leverage between pedal and lever / foot and pedal, so that "not even a millimetre" on your lever could translate to and inch on the pedal.
my original statement stands.. its liquid in a pipe.
Now back to the topic of how brilliant PD are for the direction 0 abs is going please
Of course they're hydraulic, and yes braided hoses, mono-bloc billet calipers and other rigidity-focused optimisations - the fluid barely moves once the pads make contact. Other brakes, including one I use every day, move significantly; over an inch in some cases. Most of that is the caliper (split, die cast) or lever flexing.
Any hydraulic system works via the incompressible pressure transduction through the working fluid. The pressure applies a force proportional to the area it acts upon - if any of that fluid's container is free to move, namely master and slave pistons, they will exert a force upon whatever they come up against in proportion to their area. In a braking system, master pistons, the bit attached to your foot or finger, are smaller in area than slave pistons, the bits actuating the pads - that results in the force applied at the master piston being increased at the slaves.
That's how the feeble force applied by your foot can stop a car, even without assistance - friction is proportional to the
force applied. It's also why "boiling" (denaturing) the fluid or accumulating water content makes the pedal go spongey: you're introducing compressible components, i.e. gases either from fluid decomposition or boiled water (brakes get hot).
Whilst a compressible "hydraulic" system will still work (pneumatics), the extra effort in compressing the working fluid reduces the advantage possible (force multiplication) and also wastes energy through irreversible compression / decompression cycles resulting from intermediate heat loss. That's why compressibility in the brake fluid makes the brakes less effective.
Again: once the pistons are "extended", most of the extra travel in the pedal is due to mechanical flex from the hydraulic pressure, either in the lines, the calipers, the rotors or any of the mountings (brake lines tend to try to straighten out). Braking is a force-dominated phenomenon, not "travel".
That's primarily why the pedals made for playing games with suck (relatively speaking); they require us to apply brakes using a linear movement, and to memorise "positions", rather than by applying a force through our foot that is directly proportional to the force applied at the tarmac, as we do in real life. Thanks to all the "pressure sensors" on our skin etc., we are actually naturally better at modulating brakes via pressure / force than by position.