I think we disagree about what should be fixed: the value of
default-directory or the directory to which "cd ~//bin" switches.
Sorry, let me clarify
Currently, `cd ~//bin` will cause the shell (Bash or similar) to change to ~/bin, and Emacs/shell-mode will change `default-directory` to `/bin`.
This bug is saying that Emacs/shell-mode should change `default-directory` to `~/bin` by default, optionally with a user option that reverts to the current behavior in case the user has in fact explicitly configured to use a shell that interprets `cd ~//bin` to mean `cd /bin` (although I am not aware of any shells that do this (except eshell, which is not relevant to this issue)).
I (mis?)interpreted your statement to mean that you think the current behavior is not a bug and should be the default (that Emacs/shell-mode should change `default-directory` to `/bin` even though the shell changes to ~/bin).