Why do cars have automatic lurch speed when the brake is not applied?

When I read your question, I was immediately reminded of the character of Lurch on the Addams Family TV show. He was anything but speedy.

biography(The_Addams_Family)

Whatch’you talkin’ ‘bout, Willis?

Do you mean the gradual drift forward from automatic (i.e. uncontrollable) transmissions?

I think most would describe that as a creep rather than a lurch. A lurch implies more of a sudden surge, such as what happens if/when a manual transmission car suddenly has its clutch engage.

Cars in neutral don’t lurch or creep forward. Cars in gear do, because an internal combustion engine needs to keep spinning, and so if the car is in gear, even with minimal engine power, it will be transmitted to the wheels.

I’m not certain, but I imagine that with an automatic transmission, it would take extra machinery, and involve a delay (especially with earlier cars when the conventional automatic transmission was being designed) to have a mode where the car was in neutral unless/until the accelerator was pressed.

With electric vehicles, this convention is being re-explored. Many EVs offer “one-pedal driving”, where when the foot is off the accelerator, the car slows to a stop. Some others (e.g. Nissan Ariya) have a half-measure, where the car still creeps forward.