As @stoicfury indicates, these aren't perfect questions in a lot of ways, but nevertheless they are valid problems in the study of logic, rhetoric and argumentation (core disciplinary functions of philosophy) and -- what I think is the kernel of the issue -- we're the only stack for which it really makes sense to ask these problems. For now, anyway.
One thing to decouple here might be that rhetoric could conceivably be its own SE, and could possibly be a good home. Which raises another point perhaps: that to a large extent these logic/language questions can be meaningfully refocused or decomposed into questions about language usage (so for the EL&U stacks and the like) and questions about pure logic (and so could be plausibly posed as problems for the maths/CS stacks.)
But the thing is still this: any 'hunt the fallacy'-style problem will still be a soft-question on those sites. It doesn't really get at core questions or problems for them the way it might conceivably for us; though maybe they are still very superficial, even for us. I sense this is what's missing "spiritually" from these questions, and what might be underlying your disapprobation: that the sense of philosophy is entirely obscured in pedantic fallacy analysis.
Of course it's not that fighting various forms of stupidity isn't valuable -- indeed, Deleuze says it's something like the principal value of philosophy to harm stupidity, to make stupidity something shameful. But fallacies are generally rather simple errors, while active/malignant stupidity, which philosophy does battle with, confuses and vulgarizes in a different and more elusive way than simple error; it poses problems poorly, mistakes the insignificant or uninteresting for the important/surprising/remarkable; it's non-sense.
At any rate -- it might well be that we do need a community ruling that hunt-the-fallacy isn't really a constructive activity for us. But I think the point would be that this would effectively be to rule it out from all of SE (at least until we have a rhetoric site in beta.) So to some degree I think we are 'due' these questions as a matter of the current structure of the SE ecosystem, because there isn't a better place for them -- which, I would just note in passing, can change very quickly.
All this said, the ground rules still apply to these and all questions on the mainpage: evaluate based on each particular case. If they're not constructive (unclear, confusing, vague, etc.), vote or flag them down. My suggestion would be to use the builtin mechanisms to help shape the overall question base in more generative directions; and if we do need community rulings around this we can circle back and try to form a consensus about what actions to take.
