Interestingly enough, I've had hydraulic brakes fail on me for two different cars (thankfully it was 20 years apart, but still I would have preferred that the first time was the last time).
iirc both times it was some sort of brake fluid leak.
So, while I totally agree that having motorized breaks is really scary, hydraulic brakes can fail as well.
I've also had two cars lose brake pressure. I'm very thankful that the cable-operated parking/emergency brake was functional on both cars; it saved one of them from going through the back wall of the garage.
The cable-operated E-brake definitely doesn't stop the car anywhere near as well as the power-assisted hydraulic brakes, but having two different braking methods can be a literal lifesaver when one system fails. (And all systems fail! I'd previously had two other cars where the E-brake didn't work.)
I've never had my breaks fail on me. I also don't use the parking break that often. I would be so proud of myself if I realized what was going on, remembered that the e break exists, and used it before hitting the back wall of my garage.
When the hydraulics failed (brake line exploded) on my old vehicle I discovered that the cable is also attached to the brake pedal, so I didn't have to play games with the parking brake mechanism. There is a world of difference in braking force though, it's like pushing on the side of a brick building to gently encourage the vehicle to stop. I was lucky that I was driving a manual so I could also downshift to kill the speed.
I had the engine fail (timing belt broke) and that also killed the hydraulics in that car, very different behaviour of the brakes compared to normal and you need a hell of a lot of pressure to stop but it still works. Downshifting was not an option since the engine didn't work anymore.
You are probably referring to the brake assist mechanism in all cars after the 90's. It uses vacuum pressure from the engine to help you push the pedal down. Without the engine running, the brakes will work ~3 times, and then they'll get super hard to press - but they will still function if you have leg muscles strong enough to work them.
I don't deny that there can be physical failures to the systems. And I also drive a hybrid currently that most of the time only uses the electric motor for slowing down, I don't find using the motor for braking scary. I personally see having both regen and hydraulic brakes on a vehicle a great step forward in redundancy and safety.
Electrical slowdown in hybrids does not provide redundancy for emergency braking. The battery has to absorb like 500kWt during 1s, this is well outside what a small battery can do.
Redundancy doesn't mean it will bring the car to a stop as quickly as hydraulic brakes, it is just another means to bring the car to a stop safely. From personal experience I could safely get my car to a stop in many situations without using the friction brakes at all.
I had _a_ brake caliper jam on my tundra. Completely frozen sliders on the caliper. The good news about hydraulic brakes is that the other circuits on the brakes still worked fine! I actually didn't realize the caliper was dead for (likely) a few months. With modern cars, each wheel is independent, so leaks and failures are more failsafe.
iirc both times it was some sort of brake fluid leak.
So, while I totally agree that having motorized breaks is really scary, hydraulic brakes can fail as well.