Note. After over one month of discussion, and more than one week of voting, I think the community has decided.
- Leave the tag alone: 43 upvotes (20.38%)
- Consider the tag deprecated, but do not remove it from the system: 12 upvotes (5.69%)
- Request that the tag be burninated and blacklisted: 156 upvotes (73.93%)
So it seems like we'll be requesting that homework is burninated and blacklisted. See this question for the next (and final) steps in the process.
New users don't normally include it, whether or not their question is homework. On the list of newest questions, most are of the homework type, but few are tagged as such. If the goal is to identify or filter homework question, the tag fails at that.
Despite of 1, it is used often enough to be the top tag on the site. So it gets to be the one inserted in the page title. For example, this question is titled homework - Finding the adjoint of an operator instead of functional analysis - Finding the adjoint of an operator. The beginning of page title heavily influences the way Google treats the page (this is why the tag is put there to begin with). The (homework) tag deprives the page titles of the site from including the most important key words.
Gold tag badge confers the ability to unilaterally close duplicates with that tag (and SE might extend this ability to other closure reasons in the future). This makes sense if the badge indicates the expertise in some subject. But homework is not a subject. There is no such thing as being an expert in homework.
The tag is featured on the front page for new users, promoting the image of the site as a homework factory:
If it's too much work to delete the tag, I suggest to at least change the tag wiki to say that the tag is deprecated and should not be used. The users who wish to receive a hint instead of full solution can say so themselves. Tags are for classification, not communication.