I just tested to see what happens if you don't name a branch before leaving it. Surprisingly, despite all that scary looking text about detached head, if you switch over to another branch git will print out a message that you're leaving commits on an unnamed branch as well as instructions on how to get back and name it later (and of course the commit hash can also be recovered from the reflog).
So yeah not only is the detached head state not a broken state, it's not even really a scary state to be in.
For someone who understands git, it certainly is not. But if you are not aware of how git works, committing things when HEAD is detached could to confusion in the best case, and lost commits in the worst.
So yeah not only is the detached head state not a broken state, it's not even really a scary state to be in.