I think we should.
t1401 expects to be able to, but if you really do it:
$ cd /tmp
$ git init throwaway
$ cd throwaway
$ git symbolic-ref -d HEAD
the setup machinery considers that you are no longer in a working
tree that is controlled by a repository at .git/ because .git/ is
no longer a valid repository, so you cannot even do
$ git symbolic-ref HEAD refs/heads/master
to recover.