This is a good point you raise that has some additional story behind it.
I agree with you that there is a general misconception that surrounds exactly what a plugin is and how they are not that different than a solution without a plugin that might find its way into your standard functions.php
file.
The whole "without-a-plugin" phrase, phenomena has its origins in search engines where often people who want either,
- a quick copypasta solution
- to learn about how to perform a specific action** (a tutorial if you will)
...and or think,
- too many plugins slow down your site (my friend told me) so give me some copypasta.. ya mun!
...but have to wade through page after page of search results that return more often than not a solution to your request in the form of a plugin.
Its also a misconception that "too many plugins slow down your site". That's simply not true by default. Bad or unoptimized code is what will make your site perform poorly regardless of whether it was in your theme or in your plugin directory.
Further to that point, people who don't code for living tend to install more plugins than those of us that do. This compounds the issue by creating a situation where a user has umpteen plugins installed, from as many authors, all of which with different degrees of code-quality that can result in poor performance. This then feeds the myth that too many plugins are a bad thing.
What we get in return is {something here} without a plugin
but for which there could be more than one intent behind the question as shown, although more often than not if you're phrasing your question that way on WPSE then you probably lack the understanding surrounding the Plugin API and the API in general.
I see the issue as being Misconception born out of Miseducation
Who's fault is that?
Is it the people promoting information that's often second hand "I heard it from such and such so I'll repeat it here, there and everywhere, as if its the truth" or is the professionals like you? (I'm not professional so I'm excluded)
Only kiddin...
I don't mean YOU (Chip) in the literal sense either, I mean it generally as in US, the ones that do know (for the most part) right from wrong.
The fact that there is little consistency in where and how to refer to what is standard and best practice concerning WordPress is the reason why there are a lot of bad themes and plugins out there to begin with. The same principal extends itself to this very topic that you raise, its all relative.
It all comes back to miseducation.
What we need?
Instead of adding something to our FAQ that is about,
not asking for solutions "without a plugin"?
I recommend adding something to our FAQ or more appropriately a link from within our FAQ to a wiki reference or external article reference that explains the concept of the Plugin API and how that asking questions that are phrased with the term "without a plugin" are not necessarily the right kind of question to be asking and provide adequate reasons as to why that's the case and how that solution itself should be about the resulting code, its efficiency and overall quality and adherence to standards and best practices.
That then is aimed at making the whole notion of "without a plugin" moot.
Otherwise we run the risk of not being able to ask anything at all if the following were true,
- Plugin recommendation questions are off-topic
- Plugin recommendations as a one-line or shallow answer are not encouraged
- Questions for recommending solutions without-a-plugin are not allowed
You state,
The end goal here is building a body of knowledge and reference code/material.
Fully agree. WPSE is a wealth of knowledge, its an invaluable resource however it lacks resources that allow for technical posts that are designed to educate by way of theory, simply because its not a question-answer, so you can't exactly go create a question that provides the "why" behind the "how" that is the basis for these misconceptions in the first place.
So my question now is where and how do we go about providing supporting information that we can refer these questions to in support, along with the answers we provide, that help to further educate people about what Plugins really are and begin to have a positive impact in reversing this miseducated state of being that is spread through the WordPress community as a whole?
WPSE being a centralized body of knowledge is one of the perfect places to have these supporting references.