If the question is locked, obviously new users can't post answers to it because no one can post answers. It seems somewhat redundant to list that box there. I'm not saying remove the protection from the question just because it's locked. After all, a question can be unlocked (although unlikely). However, it is unlikely and it's just an extra box there that doesn't really mean anything on the post anymore.
Most notably for the "protected" box, it states:
To answer it, you must have earned at least 10 reputation on this site.
Yet, because it's locked, that statement is untrue.
The "protected" box should be hidden when it is not possible to add additional answers to the question in the first place, which includes when the question is locked or closed. If the question is unlocked or reopened, it should be shown again.
