Expansion of exclamation mark in single quotes in subcommand

[Maxdamantus]

version: 4.3.11(5)

This seems like a bug, but it seems to have been here for a few years
(from the git repository, bash-3.0 displays this behaviour while
bash-2.05b doesn't).

With history expansion enabled (set +H):

$ echo '!!' # good
!!
$ echo "$(echo '!!')" # not good; !! expands
echo "$(echo 'echo '!!'')"
echo !!
$ echo '$$' # good
$$
$ echo "$(echo '$$')" # good
$$