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5. Is there a minimal set of perfect VTC choices?

Also, my guess (verified by experiment, as I found out) is that getting rid of the "homework" VTC option will probably just reroute the VTC stream. You probably can't alter people's will to close questions they dislike on a site . I think the remaining options should be sufficient as alternatives to the "homework" VTC option, and they may even lead to less complaints from OPs, but they also come with problems. If the selected VTC option is "homework", often it is met by the reply "but, it's not homework". The other choice that often receives complaints is "duplicates". It is a choice that ironically can require considerable effort, and is liable to result in a dispute with the poster (starting with "but this doesn't answer my question" etc). Unfortunately, if there is a discernable question in the post at all (one that is not too broad or cryptic), and it deserves to be closed, it is usually because it is a "duplicate".

Issues such as posters complaining consume time and effort, wasting resources, in addition to potentially discouraging potentially valuable future posts.

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:

5. But, is there a minimal set of perfect VTC choices?

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:

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. How can you 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.

I don't address this last point at all. I'll just state that 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.

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.

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.

I don't address this last point at all, this point seeming close to what the OP seeks an answer for. I'll just state that 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.

6. What exactly is gauged as wrong with "low-quality" questions ending up in the "homework" bin?

What is being closed?

I don't address this last point at all. I'll just state that 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.

What is being closed?

6. What exactly is gauged as wrong with "low-quality" questions that end up in the "homework" VTC bin but are not really homework?