> copy a function with its closure

By closure, do you mean the values of free variables at the time of the copy?

If so, the inability to do a perfect copy is applicable to regular functions at the top level, too. (For such functions, other global variables are free variables.)

Considering this, I think this is why copying a function is generally defined as just having a reference to the function that can later be used to invoke it. It does not include each copy of the function having its own copy of the function's free variables from the instant of the copy. Separate invocations of the multiple copies (i.e. references) of the function may affect the shared closure environment/free variables.