On pavement, when the front brake performs well and is operated near optimal power, the back tire will not have traction. The back brake is entirely redundant in that case.

> That’s not the same thing as redundancy

It is. Redundancy doesn't necessitate the redundant option being identical to the first.

> ”Redundancy doesn't necessitate the redundant option being identical to the first.“

Yes. In fact, in a redundant system, using different designs or technology is often an advantage, so that a failure mode that affects one system is unlikely to affect the other.

But if something is redundant, it is “able to be omitted without loss of function”. Front and back brakes on a bike are not there for redundancy. They are components of the same braking system: without both in service, they don't work as well.

Or to put it another way, the front brake isn’t there as a spare in case the back brake fails. It’s there because without brakes on both wheels, you can’t stop quickly in an emergency.

> Front and back brakes on a bike are not there for redundancy. They are components of the same braking system: without both in service, they don't work as well.

Bikes are very different from cars due to the short wheelbase vs high center of gravity.

At moderate or fast speeds maxim deceleration occurs when the front tire applies enough force to lift the rear tires off the pavement thus removing the impact of the rear tires. Below maximum acceleration you could use the rear break but it doesn't do anything applying the front break slightly harder would do.

At sufficiently low speeds the rear tire can help, but it's really there for redundancy as even acting alone it doesn't work very well.

This only applies in ideal conditions (eg: dry tarmac). Where there is less surface friction (wet or icy surface, dirt or gravel trails, etc) you're going to quickly hit the limits of the tire's traction, so will need both brakes if you want to stop in the shortest possible distance.

Wet roads, cold ice, and dirt still provide enough friction to send you over your handlebars at speed. They just increase the maximum speed rear tires provide any benefit. Near its melding point ice isn’t going to provide enough friction for rear breaks to matter.

So sure there’s a minimal benefit in some very specific conditions, but no they are there for redundancy.

In reality, the rear brake contributes nothing (apart from redundancy in case of front brake failure) to being able to stop quickly in an emergency. The quickest stop is achieved by using the front brake as strongly as possible while bracing oneself to avoid going over the bars, which if done correctly, will mean the rear wheel will have next to no contact with the ground. That means locking the rear wheel with the rear brake will contribute nothing to stopping.

> That’s not the same thing as redundancy

The law literally says mechanically redundant, as in failure of one cannot affect the other.

It's illegal to have a single hydraulic system controlling both.