I think it's fine to retag (without comment) as long as it is perfectly clear that the problem is homework. In my experience, around half of the questions the community initially believes to be homework turn out, in fact, not to be so.
Let us bear in mind the description in the homework wiki excerpt:
A routine question from a textbook, course, or test used for a class or self-study.
Taking a somewhat selfish view--that is, with an attitude of discerning what is best for our community, rather than the original proposer (O.P.)--it seems that "routine" is the operative word. (Sometimes we can identify the source of a question--but not in a reliable or consistent manner--and it would be presumptuous to suppose we can tell what the purpose of a question is in the mind of its asker!)
"Routine" questions differ from those we are really interested in for several reasons, including
They tend not to have any specific application.
If any data are included, they are artificial (and often cannot be further explained by the O.P., who knows nothing of their genesis).
They tend not to have any context.
Loading the site with a gallery of such questions potentially diminishes the value of searches and other uses of the site as a reference and ongoing resource. Tagging routine questions with homework is one way to help future researchers to get great answers to the questions they may face.
These considerations take us away from having to guess why somebody has posed a question and move us toward evaluating the question on its own merits. I will immediately grant that this does not resolve the issue of what constitutes "homework," because one reader's "routine" question could be difficult or unusual for another. I suspect, though, that some questions will be so evidently routine that we should not hesitate to tag them accordingly. Some of the indications of "routineness" would include
The question has appeared in almost the same form on a previous thread and has a similar solution that requires straightforward substitutions of numerical values in its statement. (Example: almost any question calling for using the Normal distribution to convert between z values and p values.)
The question is entirely theoretical, without any applied context. (Consider whether to migrate such questions to the Math.SE site.)
Solutions are readily available elsewhere on the Web by means of an "obvious" search. ("Obviousness," once again, is personal, but I would claim that a search based, say, solely on a question's tags which turns up a solution in the first page would qualify as "obvious.")
The question is expressed in a test-like format, such as a multiple choice or to fill in a blank.
The language is imperious, as in "Find the answer,...," "State why,...," "Prove that," etc.
In such cases, readers (with sufficient reputation) ought to consider immediately adding the homework tag to the question.