Lug Nut, a hydraulic system is considered to be a type of mechanical system. Every motor vehicle has a brake system in which at least some braking capability can be applied without relying on the power brake booster and without relying on computers and software. Furthermore, hydraulic brakes in cars are required to have redundant circuits. In cars, you have a split master cylinder with one circuit acting on two wheels and the other circuit acting on the other two. The circuits are monitored to detect failures with either circuit. In the industrial automation world, this sort of thing is referred to as "control reliability", and every safety-critical circuit needs to be assessed regarding the need for this, based on a risk assessment.
Furthermore, in most cars, there is indeed a totally mechanical braking system: the hand brake / parking brake. (I don't like the trend towards having this actuated electrically by a push button.)
It is also a FMVSS requirement that the steering linkage be mechanically connected. It can be power-assisted ... but if the assist fails, it has to be possible to operate the steering manually.