Yes. Someone could drive away.

The car only checks the presence of the key when starting the car. After that it will run until it is shut off. With no key.

This is to protect the battery in the key fob. If the key fob had to keep transmitting to maintain a connection with the car the battery would run down quickly. So you'd either have to replace the battery very often, or have a much larger (and heavier) fob.

Also if the battery ran down while you were driving, the engine could shut down!

The current SKS system is a simple superset of the existing key fobs that everyone started using just over 10 years ago.

There are ways around this, but it would increase the cost and complexity of the system.