The coefficient of friction for brake pads range from a mu of 0.3 on the cheap side to 0.45 on the performance side to 0.6 on the racing side. So if brake pressures (N) are the same, then the stopping force of the brake increases (F=mu*N) with the higher coefficient of the brake pad which costs more money. Now you claim that it doesn't matter when the coefficient of friction between the tires and the roads is the limiting factor. According to many sources, the coefficient of friction between a dry surface and the average tire is 0.7. So if you do the calculations, brakes play a tremendous role in stopping the car up until the point where the tire starts slipping which is where the ABS kicks in and prevents said tire from slipping to maintain the 0.7 (or maximum) amount of friction as possible to start. How can you claim that the higher value of F applied to slowing down tire rotation isn't braking you sooner as long as the tire isn't slipping? Are arguing that a mu of 0.3 on the low end and 0.6 on the high end provide the same force at the tire? All those linked articles you quote as your evidence essentially are stating the case when your ABS is engaged.
You neglect a couple key factors.
1. It does not matter if one has a higher coefficient of friction as they are in very different contexts. IE, imagine friction of .1 with 1000 lbs of pressure vs .7 friction with 10 lbs of friction. Coefficient friction alone means nothing.
2. More importantly, brake forces don't need to be the same as you you state because you can apply more force (ie press brake pedal harder) to compensate (something I acknowledged earlier).
Your car however can not apply more downward force on the tires to the roads, so the force is fixed. This plays into how touchy or soft your brakes may feel, but we are assuming the driver with leverage from the pedal can apply adequate force.
3. Your friction math changes when you consider cars don't get the full downward force on the rear tires as the momentum pushes it forward. Same reason a front brake/tire on a motorcycle has over double the stopping ability of the back brake/tire.
4. You need to review the math in the article we linked:
https://grassrootsmotorsports.com/articles/grm-vault-grassroots-guide-braking-systems/ As I stated before, I can count the number of times my ABS has kicked in on one hand because I don't brake that hard which means the limiting coefficient of friction for stopping distance on my vehicle is the brake pad. The reason brake pads are designed to have less friction than tires is to prevent you from going into an instant skid the moment your brakes engage.
So much wrong here. If that was true, you would have never been able to activate the ABS at any point.
The limiting factor
before abs is simply your choice of force being applied to the brake pedal. Some gets lost to slipping at the brake pad and some gets lost to your tire slipping on the road. However, you have the ability to apply more force to the pedal which gets translated into friction force from pad against the rotor which slows/stops the wheels. You have the ability, in theory, to apply enough force to the pedal to instantly stop the rotors (poor car)...which would of course cause you to skid or abs because the tires can't hold the road that fast. The limit is how much force you apply to the pedal in that case. The next limit is your tires friction.
Yes, if you had a pad with a coefficient of friction equivalent of ice you would likely have issues applying enough force, but that isn't the case.
Then you also discount wear in all your arguments. Wear is an important factor in many people's average sedans and to get better wear characteristics, one must go with more expensive materials in brake pads. I mentioned driving in routinely mountainous environments and your only proof that brake fade (google it if you don't understand the concept) doesn't exist is that you drove down a mountain in a van once just fine. Brake fade in cheaper pads occurs much sooner than more expensive pads with metallic or ceramic materials.
Cheap brake pads may work for some but your statement that there is no difference between cheap and more expensive brake pads is absolutely false. There are many differences of which I have pointed out two. So please continue to refute this by telling me about your links referring to the situation when ABS has kicked in.
Our discussion up until this point was on stopping distance from a safety standpoint.
The cheap brake pads from Autozone come with lifetime warranty that you can replace for free. Pretty hard to beat that value if you are worried about wear. Organic will of course wear the fastest, but least damage to your rotor. Ceramic have less of the force you love, but also easier on the rotors. It's all trade off, but I haven't seen anything to show cheap pads wearing through faster than expensive of the same style. I did acknowledge early on that cheap metal pads will possibly eat your rotors faster.
http://www.atlautosports.com/ceramic-vs-metallic-brake-pads/