No, a vehicle would not shut down immediately if the starter broke while driving at a high speed. The starter motor is responsible for cranking the engine to initiate the combustion process. Once the engine is running, the starter motor is no longer needed, and its primary role is to start the engine again when it is turned off.
If the starter motor were to break while driving, it would not have any immediate effect on the vehicle's operation. The engine would continue running as long as it receives fuel and ignition. However, if the engine were to be turned off for any reason, such as during a pit stop or if it stalls, it would not be possible to restart it without repairing or replacing the broken starter motor.
It's worth noting that a failed starter motor is not a common occurrence while driving, and vehicles are typically designed with redundancies and safety measures to prevent sudden shutdowns due to a single component failure.