When does a function appear in .plt?

Question

I'm confused as to when a function appears in the .plt section.

I was trying to print the address of printf from inside the code (not by objdump) and I stumbled upon this problem. I wanted to "follow" printf through .plt and .got in C and with gdb.

The source for this experiment is the following (it's not "nice", but it is enough to show what I'm trying to do):

int main(int argc, char *argv[]) {
    printf("Warm up\n");

//    int (*plt)(const char *format, ...) = printf;
    int *plt = argv;
    long got = *((int*)plt);

    printf("plt 0x%016lx\n", plt);
    printf("got 0x%016lx\n", got);

    return 0;
}

objdump gives as expected printf in the .plt:

$ objdump -d -j .plt ./a.out 

./a.out:     file format elf64-x86-64


Disassembly of section .plt:

0000000000000540 <.plt>:
 540:   ff 35 72 0a 20 00       pushq  0x200a72(%rip)        # 200fb8 <_GLOBAL_OFFSET_TABLE_+0x8>
 546:   ff 25 74 0a 20 00       jmpq   *0x200a74(%rip)        # 200fc0 <_GLOBAL_OFFSET_TABLE_+0x10>
 54c:   0f 1f 40 00             nopl   0x0(%rax)

0000000000000550 <puts@plt>:
 550:   ff 25 72 0a 20 00       jmpq   *0x200a72(%rip)        # 200fc8 <puts@GLIBC_2.2.5>
 556:   68 00 00 00 00          pushq  $0x0
 55b:   e9 e0 ff ff ff          jmpq   540 <.plt>

0000000000000560 <printf@plt>:
 560:   ff 25 6a 0a 20 00       jmpq   *0x200a6a(%rip)        # 200fd0 <printf@GLIBC_2.2.5>
 566:   68 01 00 00 00          pushq  $0x1
 56b:   e9 d0 ff ff ff          jmpq   540 <.plt>

Now instead of int *plt = argv; I use (the line commented out above):

int (*plt)(const char *format, ...) = printf;

Now objdump gives:

$ objdump -d -j .plt ./a.out 

./a.out:     file format elf64-x86-64


Disassembly of section .plt:

0000000000000540 <.plt>:
 540:   ff 35 72 0a 20 00       pushq  0x200a72(%rip)        # 200fb8 <_GLOBAL_OFFSET_TABLE_+0x8>
 546:   ff 25 74 0a 20 00       jmpq   *0x200a74(%rip)        # 200fc0 <_GLOBAL_OFFSET_TABLE_+0x10>
 54c:   0f 1f 40 00             nopl   0x0(%rax)

0000000000000550 <puts@plt>:
 550:   ff 25 72 0a 20 00       jmpq   *0x200a72(%rip)        # 200fc8 <puts@GLIBC_2.2.5>
 556:   68 00 00 00 00          pushq  $0x0
 55b:   e9 e0 ff ff ff          jmpq   540 <.plt>

Where is printf? Why is it not in the .plt anymore?