I'm afraid your question is too vague for me to understand what class of questions you are referring to. I will therefore base this answer on the information you gave in your comment where you pointed out this Q&A as the one that prompted this discussion. You considered it:
[...] a made up problem, not to solve an existing issue, but just with the intention to create a broad collection of answers. That makes it a purely programmatic question [...]
Well, anything involving computers could be considered a programming question since computers are useless with no software running on them. However, basic system administration tasks like file renaming or other manipulation are right at the core of this site's topic. How could they not be?
I think you are seeing this as programming simply because you tend to use python for everything so, of course, you end up writing programs. There's nothing wrong with that but because you're so good at python, I get the feeling you're not really aware of the general purpose POSIX tools that all Linux flavors have by default.
grep (which is not a language, by the way) and
rename do not require programming knowledge to run them. The fact that you would approach an issue with a python script does not mean that the question was about programming.
The question you highlight is a case in point. It is a broad question asking about way of removing an extra character from many file names. That is a problem that i) could indeed be shared by future users; ii) can be used to highlight the abilities of the various tools making the answers easily adaptable to other problems.
I think that's where your pythonista view is clouding the issue. A python (or Perl, for that matter) script written to solve a particular problem is almost always "giving a man a fish". A solution using the core utilities available on any *nix system, one that highlights what these utilities can do, is usually "teaching a man to fish".
In other words, an answer showing a python or perl script that can rename files can be fun but it is unlikely to help someone who doesn't know how to hack in those languages already. An answer using
grep and regular expressions opens a whole world of possibilities that require no programming knowledge whatsoever except, perhaps, a working knowledge of regex.
More to the point, where would we be without these questions? Personally, I have no interest participating in a site whose questions are 90% "no wirlesses helps plase" and "black screen no X server". I find them uninteresting, repetitive and boring. They don't challenge me to find an answer. if I can give one, I either know it already or just need to spend the 5 minutes googling that the OP was too lazy to dedicate.
As for actual problems, yes, that's part of the site's mandate but not its entirety. The SE sites also aim to become a "repository of knowledge". For example, my post on U&L about replacing strings has received 168930 views at the time of writing and more than a hundred votes. There was no problem to solve there, however it serves to highlight certain commonly available tools and the things you can do with them, it serves as an answer to many similar questions. It's a reference. That is a Good Thing©.
So, in conclusion, no, the site is not only for "real" problems. It is also for imagined ones which, however, bear a close resemblance to everyday problems users might face. If you don't like these questions, just ignore them. As you can see, many of us like them and welcome them. Work on others if you don't. There's room for all of us! :)