However, Perl seems to very stubbornly insist on using 32 bits for each character.

That's not true.

ASCII characters require one byte.
Other iso-8859-1 characters require one or two bytes.
Other Unicode characters require up to four bytes. (Usually two. Practically, never four.)

Both Devel::Size and a peek at the size of the internal of the internal show differently.

$ perl -MDevel::Size=total_size -E'say total_size("A" x 1024 x 1024 x 
+100)'
104857636

$ perl -MDevel::Peek -E'Dump("A" x 1024 x 1024 x 100)' 2>&1 | grep LEN
  LEN = 104857604
[download]

The rest of the memory was used to build the string and is available for reuse. There's also the possibility that you are making a copy of the string by using it as the return value of the file. (Do you see a difference from appending ";1"? I'm getting 0 from time.)