[A part taken from Physics SE.]
I agree. Screenshots of text have no place on this site.
There is simply no reason that plain text should ever be presented as a screenshot, and plenty of reasons why it shouldn't. If you want to quote text from a separate source which you have as an image, it is your responsibility to transcribe it.
Transcribing the text, simply put, makes the site easier to read for everyone. It might make things more awkward for the reader by just a little bit, but it's definitely there and it's your responsibility to make your posts as readable as possible.
More importantly, it is an important accessibility concern. Do you have good eyesight, and are you reading this site without accessibility tools or without zooming in on text? Then good for you! but not every user of the internet has that ability. There are plenty of people with visual impairments, going from difficulty reading all the way to complete blindness, that have every right to use the internet, which they do relying on assistive technology such as screen readers that do just fine if text is typeset as text, but which get stopped in their tracks when it comes to screenshots. Using proper typesetting (including good use of Markdown and MathJax) provides additional HTML syntax that those assistive technologies can use to give a more meaningful account of the content on the page.
There are some disciplines that are intrinsically hard for visually-impaired people (say, photography? though even then, there are surprises) and physics is not one of them. I would like this site to be open to all, and proper typesetting is one of the things that allows us to be that.
This machine-readability also makes the text easier to register and index by search-engine crawlers, which makes the post easier to search for and easier to find by other users, and which therefore makes the post more useful for a broader cross-section of internet users.
On a separate track, transcribing the text in your question is a way to demonstrate that you're prepared to match the effort you're asking others to perform in researching and writing an answer to your question with an effort to the best of your abilities to write the best question you can. If you cannot be bothered to type out two paragraphs of text, which then means that prospective answerers need to spend extra time squinting at a smudgy screenshot, then that speaks very poorly about how you value the effort you're soliciting.
This specific thread is explicitly about text, which has no entry barriers to transcribing. Quite often, though, screenshots of text will also include some mathematics, which do require learning to use the $\LaTeX$ syntax used by the site's MathJax engine. I do not think this is an excuse: if you want to quote mathematics, it is your responsibility to typeset it accurately. This is indeed an entry barrier, and you do need to learn how to do so - the Mathematics SE site has an excellent tutorial - which goes back to putting in the effort in formatting your question correctly, to match the effort you're expecting from the answerers.
(Furthermore, using the correct MathJax to display the math is even more of an accessibility concern. MathJax output is displayed using MathML, which contains a ton of semantic information that can be used by screen readers. To see just how much, right click on any complicated formula (here's one for convenience, $f(x) = \sum_{n=-\infty}^\infty c_n e^{inx}$) and click on Show Math As > MathML Code (so, for my example, it produces this code, which is the 'true' internal representation of the maths as the browser understands it). The resulting mess is not meant to be human-readable (the way $\LaTeX$ syntax is) but it is a bonanza for an automated system.)
Now, from time to time (and in practice quite often), community members might step in and transcribe an image for you, particularly if you're a new site member. That's great! somebody decided to help you out and help improve the site on their own. However, if this happens more than two or three times, then it quickly starts becoming abuse of the site's community mechanisms. You are responsible for the content you post and for ensuring that it does not unduly waste other people's time, either editors or readers.
As to what this community should do with questions that contain screenshotted text: what we've been doing already, namely downvoting and, where appropriate, closing; leave a link to this thread if you feel like the downvote requires an explanation. If you have the time and inclination, transcribe the image, particularly if it's a new user, but do make it clear to the poster that they should be doing that on their own.
I use the AutoReviewComments userscript and I've added a link to this answer to my copy of the 'Text, not pictures' template, which now reads
Text, not pictures
Please do not post images of texts you want to quote, but type it out instead so it is readable for all users and so that it can be indexed by search engines. For formulae, use MathJax instead.
and as copyable source
### Text, not pictures
Please [do not post images of texts you want to quote](https://meta.stackexchange.com/questions/320052/why-are-images-of-text-code-and-mathematical-expressions-discouraged), but type it out instead so it is readable for all users and so that it can be indexed by search engines. For formulae, use [MathJax](https://math.meta.stackexchange.com/q/5020) instead.
This takes a lot of the friction out, and it makes it much easier to autocomment, downvote, and then move on with one's life.
And to deal explicitly with the specific question: is the presence of a non-transcribed screenshot of text, by itself, reason enough to close a question? Frankly, I personally think that that is excessive and not a very effective way to tackle the problem. As I said, I think that screenshots of text have no place on this site, but the close-fix-reopen cycle is too sluggish to deal effectively with the problem.
More importantly, though, for the vast majority of questions that fall in that category there will also be other, more established, reasons to close the post, which makes the question moot most of the time. If none of that is applicable then, in my view, the first action should be a sharp word and a pointer to this thread. Typically the screenshot will be fixed one way or another, but if a newcomer insists on forcing others (by their inaction) to transcribe their screenshots then question closure becomes a more appealing option as a way to force them to take notice.
Ultimately, of course, people's votes are their own, but to offer a definitive guidance proposal: vote to close on any other applicable reasons first, and if none are applicable for me the relevant question is: does this question's use of a screenshot constitute an abuse of this site's community mechanisms that can be effectively dealt with through a question closure? If the answer is yes, then I'd say a custom-reason closevote pointing here is warranted.
