Remove unused section using objcopy

Question

Suppose I have the following source file:

// file.c:
void f() {}
void g() {}

I compile it into object file using gcc -ffunction-sections:

$ gcc -c -ffunction-sections file.c -o file.o
# It now has at least two sections: `.text.f' (with `f'), `.text.g' (with `g').

Then I try to remove section .text.g (with g) from object file:

$ objcopy --remove-section .text.g file.o
objcopy: stQOLAU8: symbol `.text.g' required but not present
objcopy:stQOLAU8: No symbols

So, is there way to remove function-specific section from object file (compiled with -ffunction-sections)?

Extra info:

1. Full list of symbols in file.o is:

   $ objdump -t file.o 
   
   file.o:     file format elf64-x86-64
   
   SYMBOL TABLE:
   0000000000000000 l    df *ABS*  0000000000000000 file.c
   0000000000000000 l    d  .text  0000000000000000 .text
   0000000000000000 l    d  .data  0000000000000000 .data
   0000000000000000 l    d  .bss   0000000000000000 .bss
   0000000000000000 l    d  .text.f        0000000000000000 .text.f
   0000000000000000 l    d  .text.g        0000000000000000 .text.g
   0000000000000000 l    d  .note.GNU-stack        0000000000000000 .note.GNU-stack
   0000000000000000 l    d  .eh_frame      0000000000000000 .eh_frame
   0000000000000000 l    d  .comment       0000000000000000 .comment
   0000000000000000 g     F .text.f        0000000000000007 f
   0000000000000000 g     F .text.g        0000000000000007 g
   

2. My goal is to eliminate some sections from object file similarly to what ld --gc-sections does.

Or is there some theoretical reason why such task is absolutely out of the scope of objcopy and can only be performed with ld -r?