Why is the function return in C a statement?

statements alter the status of the machine

Except when they don’t. There are statements in C that have no side effects.

A statement is also a syntactic construct - it’s not about whether it has side effects or not, it’s about where it fits in the language grammar.

It changes the call stack and program counter. It puts the return value in a known place (depending on calling conventions)

Even if you don’t use the return value, the compiler still needs to store it somewhere as it may be called from different compiler units that are unknown.

When a program is running, the CPU needs to keep track of where it is in the code. This is done using a 'register' that is called, variously, a program counter, an instruction pointer, an address register or any one of a number of other, similar names.

The value in this, just like that in any other register or memory location, constitutes part of the "status of the machine." Furthermore, it is probably the most important 'status' with regards to running a program.

When your program executes a return statement, the value in this 'address register' is changed - to a value that corresponds to the piece of code immediately following the call to the function from which your are returning.

The return statement also (almost always) changes a number of other registers that comprise the status of the machine; for example, the stack pointer (if used) will be reset to its value before the call to the function was made.

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^{Note: I have grossly oversimplified the CPU-level, run-time mechanics involved in calling (and returning from) a function here; however, the 'example' will hopefully illustrate the point that the return statement must affect the "status of the machine!"}