I think challenges of this type are a great idea ... but NOT posted as questions on the main site.
TL;DR: encouraging creativity within certain pre-set guidelines is a great idea, but puzzles should be posted as puzzles, their answers as answers, and asking people to create a puzzle of a particular type would be way too broad as a question. Let's instead do this within the framework of the fortnightly topic challenges. We've already had one unusual topic challenge which wasn't based around a single tag; later on we could have topic challenges along the lines of "create an 8-line riddle with the solution 'top'" or whatever else strikes people as a nice idea with sufficient restrictions.
More detailed reasoning follows, along with various pros and cons.
There were two main considerations which inspired me to come up with the above:
Let's assume we did what you're suggesting, and posted a question on the main site which was basically "construct a puzzle satisying criteria XYZ". Then people would post their puzzles as answers to this question, but where would solutions be posted? There would be no way to answer these puzzles except perhaps in comments.1 Someone might construct a really complex multi-stage puzzle which fit the criteria, but nobody would ever be able to post the full solution in order to check that the final answer is indeed what it's supposed to be.
(A counterargument to this would be that as well as being posted as answers to the 'puzzle creation' thread, such puzzles could also be posted as questions of their own. But if they're going to be posted as questions on the main site in their own right, then why have a question on the main site where they can also be posted as answers? Let's save the latter for meta.)
Any question along the lines of "construct a puzzle satisfying XYZ" would necessarily be way too broad, and have no single correct answer. There could be an unlimited number of equally valid answers, limited only by the creativity of PSE users (which seems to be pretty much boundless), and no real way of picking a single 'best' one to be accepted.
(A counterargument to this might be that some SE sites are fine with questions which would normally be textbook "too broad", so broadness doesn't necessarily throw an idea right out the window. Take a look at Math Overflow's [big-list] tag or, to be honest, most of the questions on Worldbuilding. However, here at Puzzling we've traditionally been pretty opposed to "too broad" questions, or puzzles which could take multiple equally correct solutions. We even have a special close reason which could be pretty much covered by "too broad".)
Some more random thoughts about this proposal, which occurred to me before the above two points:
I really like the idea of encouraging creativity within guidelines. Some of the puzzles here are created because a random idea strikes someone and then they manage to turn it into a puzzle, but to make a puzzle under pre-determined conditions is more of a challenge. It would be interesting to see what people come up with.
But again, that's exactly what we do currently with topic challenges. There's no need to create a new type of question on the main site for this.
The proposal would enable people to get +10 for an upvote on a puzzle they've created. This is of course a long-standing issue on Puzzling - since writing a puzzle often takes more skill than solving it, it would be great if questions were rewarded at least as much as answers. Allowing people to post their puzzles as answers would enable them to get +10 rep for each upvote.
But this issue has already been at least partially solved by the proposal of 'wrap-up' self-answers on particularly interesting puzzles. I don't think we need the new proposal for this.
A couple of important notes on precedent:
There has already been a question of exactly this type (post a rhyming 4-8 line riddle with the solution "flower"), and it was posted here on meta, not on the main site.
Another meta post, now closed and deleted, consisted of a few ideas for a riddle with the solution "Billingsgate" followed by a request for help with completing the construction of this riddle. I flagged it for migration to the main site as a puzzle-creation question, but my flag was declined by a moderator with a note that "as this question reads "build a riddle with the word billingsgate," it's a really bad fit for the main site".
1 I seem to recall making this exact same point before, somewhere here on PSE meta. If I can work out when and where it was, we may discover that a similar proposal has already been made at some point!