It's really quite simple why this device was/is called the "emergency brake"; it is because the actuation mechanism is completely independent of any other system (such as the hydraulics) that controlled the normal braking. Thus, it could be used in an emergency situation when the hydraulic brakes failed...something once all too common.
Remember in the 1950s and into the 60s for many low-end cars, there was a single-system hydraulic unit that controlled the brakes. One failure of any kind, and you have no brakes at all. Enter the dual-braking circuit, with independent hydraulics such as if one failed the other still worked.
I remember quite clearly, going down a hill at night on the E8 autobahn approaching Pforzheim, Germany as a teen in 1971. I was riding shotgun in the front with my uncle driving. As he began to brake and downshift, he realized that the [single braking hydraulic system] on the Ford Taunus we were in failed. Luckily, his skills as a driver came into play, and he gently grabbed the emergency brake, and by using that and downshifting, we were able to come to a safe stop. The car was towed to the local Ford dealer and brakes repaired the following morning. The culprit? a rusty brake line burst.