git init respecting GIT_WORK_DIR

should this be expected behavior?

-----DOC

       core.bare
           (snipped)
           This setting is automatically guessed by git-clone(1) or
git-init(1) when the repository was created. By default a repository
that ends in "/.git" is assumed to be not bare (bare = false),
           while all other repositories are assumed to be bare (bare = true).

-----PROBLEM

[cr@extOFme-d0 ~]$ export GIT_DIR=gitdir.git GIT_WORK_DIR=workdir.work

[cr@extOFme-d0 ~]$ git init
Initialized empty Git repository in /home/cr/gitdir.git/

[cr@extOFme-d0 ~]$ git config core.bare
true

[cr@extOFme-d0 ~]$ git config core.worktree
[cr@extOFme-d0 ~]$

-----SUMMARY

i think git should not be so restrictive in what it considers to be a
bare repository.  when you use --work-tree:

[cr@extOFme-d0 ~]$ export GIT_DIR=gitdir.git GIT_WORK_DIR=workdir.work

[cr@extOFme-d0 ~]$ git --work-tree="$GIT_WORK_DIR" init
Initialized empty Git repository in /home/cr/gitdir.git/

[cr@extOFme-d0 ~]$ git config core.bare
false

[cr@extOFme-d0 ~]$ git config core.worktree
/home/cr/workdir.work

everything works as expected.  "git init" should respect GIT_WORK_DIR
env variable and set core.bare and core.worktree appropriately.