For several reasons:

1. Bike wheel rims get dirty and wet when riding (especially off road). A dirty wet rim doesn't work as a friction surface very well. Because discs are near the hub, they avoid most of the spashback and remain cleaner.
2. Bike wheel rims are made of thin aluminum. You can't press too hard on a wheel rim or it will bend or tear. Brake discs are made of thick steel, and can withstand a lot higher loads without breaking.
3. Because of the steel disk, you can use a more aggressive brake pad. Rim brakes have rubber friction pads, while disc brakes have ceramic pads which create a lot more friction. Using ceramic pads on a rim would quickly destroy the delicate aluminum.

Rim breaking actually has a mechanical advantage, being closer to outside of the wheel gives it a longer moment arm and more stopping power for the same applied friction force. But the fact that rims are so delicate means you can't use very much friction force, while a disc brake can withstand much higher load.s

Because the disc rotor is an easily replaced component, there's no concern about it wearing out, so disc brake pads can use more aggressive materials to increase friction between the pad and rotor.

The material is pretty similar to what you get in car disc brakes. The only real advantage of a disc brake is that it's further away from the tyre / road / track, and therefore doesn't get as wet and dirty, which in turn improves brake performance.

You are correct when the rim is clean and dry.

Here are some reasons to prefer disc breaks

https://cyclingtips.com/2022/06/a-complete-faq-to-disc-brakes/

In theory you are correct - there is more potential power available in a decent set of rim brakes than a hub mounted disc brake due to the longer braking track providing more friction and more mass for cooling.

This is why Maguras hydraulic rim brakes were so popular in the late 90's and early 2000's - disc brake technology hasn't really matured at that point, and hydraulic rim brakes gave advantages in modulation and power over cable actuated v brakes.

I more recent years mountain bikes have switched over almost entirely to disc brakes (either cable or hydraulic), and road cycling is starting to convert because while rim brakes have some advantages in theory, in practise these advantages are very small and unnecessary, and the hub mounted disc format provides some other big benefits.

In terms of raw power, it just isn't necessary in most cases. Even a fairly basic v type cable rim brake can lock a wheel completely solid with little effort, so what we are looking for is modulation and control - the ability to fine tune how hard the brakes are applied, which hydraulic systems give better control over (as the fluids won't compress as you pull the lever, while cables can stretch).

Looking at the components themselves, a solid disc means the pads push against something completely solid and incompressible, while a wheel rim means they are pushing against a hollow section which can flex under pressure. Similarly the disc brakes caliper is one solid piece, while a rim brake has arms mounted to opposing fork legs or seat stays which have some ability to flex.

And then there are the big practical benefits that are nothing to do with stopping power - moving the disc away from the rim gives you far, far greater mud clearance, and stops your brakes becoming useless after one muddy puddle. The same also means that slight damage to a rim will no longer jam a brake (and the brake is much better protected from damage itself). Separately you also gain the ability to design rims without any need for a braking track - so mountain bike rims can be made stronger, and road rims can be made more aerodynamic, and without any worry or concern over having to form a braking track in carbon fibre (which generally sucks).

So while there are some theoretical benefits to run brakes, they are vastly offset by the very real benefits of discs in most use cases. They have all of the power and modulation we need (noting that a lot of riders even use smaller 160-180mm rotors over the 200mm+ of the big gravity riders), with other benefits thrown in.

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The stopping distance on a bicycle doesn’t depend on the break performance as much as the amount of traction available. Breaking too hard will simply lock the wheels, especially in the wet. Disc breaks were introduced for bmx bikes due to improved performance in the mud. On road bikes disc brakes are overkill, add weight, are more difficult during wheel changes and are more complicated to maintain not to mention that the bike frame needs to be modified for them. All in all much more expensive.