Why is the shell not part of the operating system itself?

Answer 1

Operating systems do 2 things:

(1). Providing an easier abstraction layer (system calls) for user programs to access the real HW machine.

(2). It manages the system resource.

It this view, the shell is not considered as part of the operating system because:

(1). It acts as a interpreter(from user command to system calls) only, and

(2). It runs in user mode, and

(3). It is highly possible to replace the shell if you don't like one.