NO!
I'm one of the 5 users that have the Socratic badge, so I'd consider myself fairly experienced when it comes to writing challenges. I'm afraid I will sound like an arrogant jerk here, but this is what I mean:
Yes, some challenges are not flawless. Accept that they are posted on main, or loose all the good ones! We should all still downvote and close if the challenge is bad, but we have to accept that they are posted. We must remember that this site is absolutely worthless if no one writes challenges. We can't kill the fun for those who do. (And it's not like the good challenges go unnoticed because there are so many bad ones. We can handle a few bad challenges.)
If you don't want to read it all, please skip to the last paragraph!
Looking at my top 50 code-golf challenges, only 2 or 3 went through the Sandbox before I posted them. I'm not claiming those challenges were all flawless, but the errors were in most cases fixed fast and to little annoyance to other users (yes, you can all probably point to challenges I've written that had many flaws, but most have been somewhat OK at least).
If I look at my Sandbox record, I find 38 questions, 14 were never posted (only one was a dupe). The 14 I didn't post were mainly optimization, king-of-the-hill, cops-and-robbers and similar challenges that I already knew weren't ready to be posted, and I knew I had to get some assistance to make the specs waterproof.
The challenges that were upvoted in the Sandbox, and that I ended up posting have a lower average score than my other challenges.
But my main argument, and this is a big one:
I enjoy writing challenges, I like the upvotes, and I like when people answer. Not because of the rep, but because that means someone appreciates the effort I made when writing it (and the idea behind it). There are people out there that are having a good time because I wrote a challenge. When I've written a challenge, I want to get that "feeling" straight away. I don't want to wait patiently a couple of days and hope a few users read it and make a comment or two and then post it. The joy of writing it is long gone.
If I had to wait two days before I could taste the cakes I bake, then I'd stop baking cakes1. If the community were to decide that all challenges must go through the Sandbox then I'd stop enjoying it, and I would stop writing challenges. I'd guess I'm not the only one.
1I don't bake cakes, but you get the point.