The OP left me somewhat unclear about what answer is sought, which may be appropriate given the long winding history of the "homework" close topic (not to be confused with the deprecated "homework" label).
At least two questions can be identified in the OP and other answers. I'd summarize them as:
What should and should not be closed?
Are there questions that are being labeled "homework" and shouldn't, and if so, what are they? (And, should we care? - see question 1)
The first question reflects what this website wants to be.
As Gaurang Tandon points out, the tour page states that this is "build a library of detailed answers to every question about chemistry." Others argue that the aim is to build a repository of high-quality research-grade Q&As.
The second question is self-explanatory. It's about this odd VTC option that has become the "misc" pile among the "out" (VTC) bins: what's going in there? What should be going there? Should we have more bins?
Many posts I've read (linked by the OP) suggest that point #1 should be settled, and that discussions about how many and which "out" bins to have is a task that need only be settled afterwards. In other words, first draw up a constitution, only then write laws and decrees that fit into that framework. Makes sense.
Despite this, since the OP question focuses on question #2 (the homework label, its purported function and true use), I address the first point only in passing and focus my thoughts on the latter.
(Please consider this "essay" a work in progress as I learn more about what this is all about and find myself shifting in opinion on some subjects.)
Who's being closed?
There is the issue of how all this affects people posting questions.
At least one aspect of the closure process appears important to consider:
- How important is the reaction of posters to closure
Since there are no guarantees of a question being answered or even accepted when posted on this site (the only guarantee being civilized conduct from other users), closing questions becomes analogous to limiting membership in the club of acceptable ones (a self-evident truth). This just emphasizes that the available VTC choices and other exclusionary measures are an important way of defining what the website wants to be (also a somewhat self-evident truth).
Who's closing?
This site is populated by a large and presumably diverse group of people varying in their proclivity to employ the VTC option. In fact, it seems usually a small subset of all users who bother to apply this option at all. It is in itself interesting to know who these people are and why they are inclined to use the option. They are one of the groups Gaurang mentions in his answer, and their behavior is obviously central to the proper function of the VTC mechanism, to the extent that it is important. Since this active group is small, it would seem in principle that it should not be hard to enforce a uniform policy, provided one can be agreed on. But the group is potentially varied in their opinion how the option should be used.
So it leads us naturally to wonder, what are they doing, and why, with the VTC options they have been handed?
A slew of additional questions can be asked surrounding this. Some of course double back to the original question of what the site is all about.
- What are legitimate reasons to vote to close (irrespective of actual current VTC options), and how does the choice of reasons to close reflect on the goals of this site and its membership.
You can't expect its users to apply rules properly when it is unclear what those rules are. And even if there are rules, how can you ensure that users follow them? This is one way ambiguity wrt the "homework" VTC (or any VTC for that matter) can become a problem. It becomes a tool for users to operate outside of the scope of what's considered the norm, as set by the goals of the site. People will close questions they don't "like" ("like" being a catch-all for whatever mechanisms they employ to judge a question unworthy), an ambiguous term for an ambiguous process. I echo opinions I've encountered during my readings on this subject, indicating that "effort" and similar terms are poor descriptors of the property that triggers the VTC urge.
- But, is there a minimal set of perfect VTC choices?
I'd guess (probably correctly): no.
What is being closed?
So, subsets of the community regularly agree that select questions should be closed because they are of "low quality", applying the indirect and potentially misleading "homework" VTC. This leads to one important question posed by the OP:
- What exactly is gauged as wrong with "low-quality" questions that end up in the "homework" VTC bin but are not really homework?
I suggest that "duplicates" make up one significant group. Assuming these ambiguous questions should be closed, one reason the "homework" VTC is applied to these questions is because it saves effort identifying duplicates, an effort the OP should have made in the first place.
Finally, in what follows I attempt to address one question in your post a little more directly, based on what I've learned so far:
What would our closing system lack without the current 'homework close reason', should we ever get to get rid of it?
This is related to questions (1) and (2) above in my answer. In particular, I am not sure you can come up with a satisfying answer to this without first answering (1) (as Gaurang Tandon's answer also suggests).
In any case, an experiment was apparently performed not so long ago to answer precisely these questions. The result is summarized here (I need to add links - this may happen in due time):
BASELINE
Questions Closed: 378
Questions Asked: 984
Close percentage: 38.41 %
Closure statistics
Close reason, no. closed (% of total), no. edited (% of closed), no. reopened (% of closed), no. edited and reopened (% of edited)
too broad, 55 (14.55%), 8 (14.55%), 2 (3.64%), 1 (12.50%)
off-topic other (custom), 11 (2.91%), 2 (18.18%), 0, 0
--> off-topic homework, 174 (46.03%), 11 (6.32%), 3 (1.72%), 2 (18.18%)
off-topic medical, 5 (1.32%), 0, 0, 0
duplicate, 45 (11.90%), 4 (8.89%), 3 (6.67%), 1 (25.00%)
unclear, 72 (19.05%), 10 (13.89%), 2 (2.78%), 1 (10.00%)
opinion-based, 9 (2.38%), 0, 0, 0
AFTER REMOVING HWK CLOSE OPTION
Questions Closed: 325
Questions Asked: 855
Close percentage: 38.01 %
Closure statistics W/O HWK available as close reason:
Close reason, no. closed (% of total), no. edited (% of closed), no. reopened (% of closed), no. edited and reopened (% of edited)
too broad, 53 (16.92%), 1 (1.82%), 0, 0
off-topic other (custom), 107 (32.92%), 5 (4.67%), 1 (0.93%), 1 (20.00%)
off-topic medical, 8 (2.46%), 1 (12.50%), 0, 0
duplicate, 55 (16.92%), 1 (1.82%), 0, 0
unclear, 82 (25.23%), 18 (21.95%), 4 (4.88%), 4 (22.22%)
opinion-based, 10 (3.08%), 1 (10.00%), 0, 0
off-topic (other SE), 2 (0.62%), 0, 0, 0
Seems what happened is that people opted to close with "off-topic other" when homework was not available. Little else changed. The remaining options did not absorb many of the questions that would have been tagged as homework. This evidently required more effort from moderators to process (did it?), so it was not a positive result (interesting, useful even, but apparently not positive). However, my reading on the subject did not fully clarify the reason why this was regarded as a bit of a failure (was it?).
The OP suggests that homework may be capturing non-homework problems because an appropriate VTC label is absent (even though choosing labels is not something you want to discuss right now, if I understand correctly). In addition, and perhaps more importantly, these questions should not be closed. Both of these are bad things (I agree that certain kinds of ambiguity are bad). Certainly this is bad insofar as it leads to friction between the actions of a potentially rogue or misinformed subset of VTCers and the standards defined by the community. On the positive side, at least VTC has one advantage over downvoting: it is transparent.
Conclusion: an ode to closing
This is in fact not an ode to closing. I've applied closing sparingly in my time here. Other sites (SO) are militant about closing. It is a badge of honor to have closed as many questions as possible.
After considerable thought and reading, I think I finally figured out what the OP is about: people are using the "homework" VTC to close questions they don't like but are not really what you might call homework. What are these questions and should they remain unclosed?
I more or less agree with everything Gaurang Tandon has written in his answer (except the strange opposition to repetitive p-chem calculations :-) - repetitive organic reaction mechanisms are ok?). In particular I like that he bothers to attempt a defininition of what should be closed, even if one might disagree on specifics.
I've come to the understanding (possible false) that closing exists as a quick initial sorting mechanism to optimize use of resources by responders, and it is probably the closest to a reflection of what the active community (and designers of the site) think the composition of questions and answers should be.
It is important to have an official policy, even though implementation in such a decentralized unsupervised environment is very difficult: the tone in this site fluctuates and seems more a function of the whims of those present at any particular moment than of the quality of the questions, or of any particular policy. Also, it is not clear to what extent users are properly instructed on standard policy.
The editorial power of the active community provides an initial kick to good Q&As and trips up ostensibly poor ones. And it saves data storage resources down the line as the worst are destroyed.
Upvoting should in principle be enough to make the good answers surface to the top and show up atop searches, which will further encourage voting on these (and presumably reinfocement through further upvotes).
One point I make in this answer is that giving the VTC option to some of the regulars on this site is akin to giving a gun to a trigger-happy nut. You can provide them with instructions but it's unlikely to make a difference.
Aside
Shutting down:
Closing: