There's always some question or another on hold with a few downvotes on main, and they are usually created by users with 1 reputation. So if there was a small reputation requirement (eg 10) for making a question, this would be fixed. Would this be a good idea?
There are a few reasons I think this is a bad idea, any one of which I think can stand alone. Considered together, it seems like an obvious conclusion to me.
Ask Questions, Get Answers
This is what the whole platform is about. Anyone can ask a question, and anyone can answer it. It's literally the foundation for the Stack Exchange model. If we're seriously considering this, we might as well find another platform to do it on, because this feels like spitting in the face of our gracious (and patient) hosts.
But we're not a Q/A site!
An often-used reasoning to changes made/proposed here is that we aren't a typical question/answer site. And it's true, we're not. Often, the challenges here take much more preparation than a question somewhere else. Especially the good ones. It's a lot like good answers on other sites.
But there's no reputation requirement to answer on other sites, is there? So how do they stop all the bad answers by new users? They moderate, just like we do here. If it's not a good challenge, you downvote, close, comment, or whatever the appropriate action is. You don't just bar the door and hope they go away. Because they will go away.
Pearls, Not Sand
In a fairly well known article, Jeff Atwood laid out the reasoning for some of the site mechanics. The point was to optimize for (good) answers, which are the "pearls" among the vast "sand" of questions.
You might argue that our pearls are the challenges themselves (I certainly would). A good challenge often brings out very unexpected solutions. Yes, we get some questionable-worth posts from new users, but so does literally every other site on the internet that allows people to post anything. What we're looking for are the good ones, and you won't find those if you lock the whole thing up. Because people don't like to be told they don't know how to post a question. Right or wrong, it's not human nature, at least as far as I've ever seen.
Martin made a comment on another discussion about this (and Alex included it in his answer), saying that the signal to noise ratio for new users is pretty high, and this is almost certainly true. Not unexpected, but true nonetheless.
But yes, there are some notable exceptions: Doorknob, Helka Homba, flawr, Zgarb, and Joe Z to name a few. As you might have guessed, what they have in common is that their first post here was a challenge, not an answer. Not only that, but those five users combined have asked almost ten percent of all questions on the site.
So yes, there's lots of noise, but we still need that signal. Would those users have stayed if the first thing they saw was "you can't post this yet"? I don't really know. I'd like to think so, but I'd rather not find out the hard way. The problem is that you would have no idea who you're turning away. I'd rather take out the trash on a thousand bad posts than risk missing a user like any of them.
Some users don't answer in PPCG, and yet can be great challenge writers. Why restrict when there's no need to?
(Still not entirely convinced on this, but I'll make the argument in favor.)
On Q&A sites, the point of posting a question is to get help, to ask a question and get an answer. There shouldn't be a barrier to asking a question. However, in the context of creating and posting challenges, there are many more things to consider.
For this reason, it may be a good idea to require some familiarity with the site in order to post a challenge to the main site. The easiest way to do that would be to require potential challenge authors to have earned at least 2 reputation on this site before being allowed to post questions. This would require one upvote on one answer or one accepted edit. Note that "on this site" implies that an association bonus wouldn't count toward this privilege.
This would also help reduce the number of blatantly off-topic questions we get.
As Martin mentioned in the comments when I proposed this as part of We're not a Q&A site. But what should be done about it?, it's quite rare that someone posts a decent challenge without ever having participated in one. Of course there are notable examples, such as Helka Homba, but again quoting Martin,
At least subjectively the signal-to-noise ratio in challenges posted by people who never participated in one is a single-digit percentage. While there are some notable exceptions, I do think this would greatly reduce the noise we get. If someone is actually determined to post interesting challenges, I don't think posting one measly answer is going to hold them back.
Does this discourage users from posting challenges? Not entirely. The Sandbox no longer has a reputation requirement for posting, so users can post their challenge ideas and get feedback. In the meantime, all they would have to do is make one edit or post one answer before they would be able to post freely to main.