"What's the next number in this sequence?" questions, and my grudge for them

Question

NOTE: This is a rant expressing my feelings about "the next number" questions.

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Where to start?

Introduction

Puzzling.SE is a site about unique content and possibly derivatives from that content, if they are unique enough.
However, "sequence" questions as I call them are a perfect example of.... not this.

Issues

The issue I have is that they are easy to make, and usually don't require a lot of thinking.
You can think of any sequence, make a number for it, and then deny any answers that aren't said number. There are infinite mathematical theorems that could work for one series given, and so there are infinite unique answers that could be given.
This, of course, isn't what Puzzling.SE is for.
This issue is sort of like the whole lateral-thinking problem: people are using that tag to justify nonsensical answers.

Puzzling.SE, like the whole StackExchange family, is a Q and A site: ask a question, get an answer. The problem with these sequence questions, however, is that they could have any answer. This is a completely random sequence I made up in my head: 6, 7, 20, 46, 100

I bet you, if I posted that, not only would I get upvotes, I would be able to only select one answer, even though all the others are valid. This is the problem with lateral-thinking, and the problem with sequence questions.

Fix

Simple: don't allow these questions on Puzzling.
And if it's a lack of moderation that causes these to flourish, increase moderation.

Conclusion

My opinion is that sequence questions do not express the creativity of this site, and should not be allowed / should be marked off-topic or too broad.
If you agree or disagree with me, feel free to reply to this question explaining why.

Answer 1

Do not ban Number-Sequence questions

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Low quality questions like these are already not allowed on the site. Like you said, there are too many valid answers, and you can flag these puzzles as Too Broad because of that. There is no need to have a ban on these sorts of questions, since...

....Not all sequence questions are bad.

This question is a good example of a sequence question that isn't too broad - although there are a few possible and valid answers, there is one answer that is clearly the most correct. If we disallow number sequence questions on the site we would be taking away a number of high quality, well thought-out questions.

On the other hand, consider this question - not one answer here is more correct than any other, so the question is too broad (and has been closed for that reason).

The system we currently have can handle bad number sequence questions, so I don't see a need for prohibiting them. It is up to us to recognise the difference between good and bad questions, and to utilise the tools we have (flag/down-vote or up-vote respectively) in order to maintain a site with high quality questions.

Generally, a good number sequence puzzle will contain some clues other than the sequence itself - be it in the wording of the puzzle, an image, or even the way the numbers are presented - to make sure that one answer will definitely stand out over all others, and is clearly the most correct, just like any lateral-thinking puzzle. If you see a number sequence puzzle that you think is too broad, then flag it as such.

Answer 2

'Find the next number' questions are interesting if they allow for a unique, short, surprising and compelling description of the sequence provided.

The sequence provided above (6, 7, 20, 46, 100), and any 'next number' question that is generated without any effort, fails this criterion by a wide margin and when posted should be closed. A complete ban on 'next number' questions, however, would surely deprive us from some interesting puzzles.