My opinion is that it is irrelevant whether or not something is homework. I've discussed this in the past but it seemed to cause quite a lot of upset and anger - so it's potentially a difficult issue. I'll just post my thoughts on it then:
I think it is crucially important that we do not answer questions of the form "What is 1+1" with answers like "2", or questions like "What is a happy number" with answers like "wikipedia.com/Happy_Number". Calculators and Search engines already do this job. (N.B. it is also crucially important never to refer people to search engines or calculators in answers to questions - this is a new phenomenon which is ruining the value of searching the internet. One now encounters pages and pages of "JFGI" when searching). If a question is trivial in this sense it should just be closed and ignored.
That said there are lots of computations in mathematics which are do-able by computer but people struggle with: An example (that has come up a few times) is base conversion, the algorithm is easy to do but many people cannot derive it for themselves (and thus, understand or correctly carry out the algorithm) because they lack the conceptual understanding. This is the case when a simple computational question hides a deep conceptual question.
Anyway the issue is treating homework questions differently than other questions. I'd argue this is a bad idea,
One strategy sometimes performed is to see the questions template, modify the parameters and give a solution for that - so as not to just 'give away the answer'. This is obviously harmful, it encourages the questioner to simply substitute their own values into your solution and watch them trickle down through what was written. It affirms the 'blank page' fears as well as requiring zero mathematical thought. It is possible that the questioner may attempt to understand aspects of the solution but if they are attempting to "cheat" this does not stop them from writing a solution that appears to have taken effort but did not.
It carries the assumption that people are actively attempting to cheat, by default. This is rude and it is easily observed treating people immaturely helps them become it. If someone does not want to put effort into working and expects somehow, to get a solution from someone online they may attempt it but they will probably not gain anything from it. Is this some terrible shame? Should the person that answered the question feel like they have done wrong? No to both. First of all the site is archived, questions don't disappear after the questioner has handed in his work - someone struggling with self study might find it useful to them in future. Also if one avoids answering the type of questions previously mentioned that reduces the possibility of this sort of cheating.
It categorizes things incorrectly. The category 'homework' could only really be useful to someone that wants to ignore homework questions. Since homework questions are equally mathematical there does not seem to be any real reason to do this. I think it would be best for tags to just describe aspects of the question - not the social setting that the question arises from. (On that note, it seems odd that people have to "motivate" their questions when they are not homework, but a homework problem is always motivated... by the requirement for grades? It's not something which should motivate mathematical problems)
You cannot verify whether a question is homework or not. There is no way to actually decide whether or not the tag is applied correctly - just a hope that they don't lie. People doing self study might be working on problems from a book and want to ask about them - but equally likely someone might set problems from a book as homework. It's also a vague term, if someone is doing homework but they need to ask about something else to solve it - does that count? That question probably doesn't have a yes/no answer.
All in all it's just a huge waste of time and it's also irritating to read all the "Is this homework? Can you tag it that way?" handshakes which are actually meta-discussion but are allowed because there's no other way to conduct them.