I'm Grace Note, a Community Manager at Stack Exchange.
Originally, I was writing this answer explaining the mechanical issues with this idea. I won't bore with details, though, but in the long run, migration (and especially chain migration) is pretty messy and this would be a mess to implement.
Today we had a meeting to discuss something we'd been brewing on Area 51, Stack Overflow Academy. The specifics of implementation may have differed, but the goal of these was the same - you wanted a place that you could help provide guidance and sculpt posts with users, an environment that allowed you to have "questions" asked not for the purpose of getting answers, but for the purpose of building better questions.
We decided to close the proposal. Right now, over on Meta Stack Overflow, they're looking into ideas on how to make it work on the Meta itself. The fact is that the Meta really should be a place to get help in constructing good questions when the basis is present, a place that we already suggest to people now and then across the network when it comes in as a support email. There are always challenges, though - for example this site itself has seen 14 threads for sandboxes which get tons of answers, which paints a very clean image of the problem of drafting/sandboxing overwhelming the rest of meta activity.
The proposal here specifically for creating a subdomain, I will for now say that this is status-declined. Not because the idea of something beyond Meta is bad, but that this particular implementation of it is, we feel, sub-par. Meta is itself an illustration of why this is - we as a network created Meta out of the tools we had at our disposal, to serve a purpose that we needed without the full instrumentation to do what that purpose itself would need. So while Meta is what one might call "sufficient" at the job, it's not the best. Going full guns to create an entire Q&A section for the purpose of sandboxing and mentoring in asking, I feel, is repeating this same mistake - it uses what we have on hand in a makeshift "It works, that's what matters" that ignores what it means to actually work. That and personally it feels about as excessive as using a grenade to clean your sink - there's way so much overhead associated with a full Q&A that goes beyond what you need for this task.
This is something that is a real problem across the network, and I feel that if we want to work on providing an in-house solution to this, we should want to create something solid and robust, that has the tools needed for the job and nothing more. We don't have this solution yet, we don't have a full plan. But it's something we'll be working on. Not "in the future", not "in the near future", this is something to be working on in the now. And while we work on it, Meta will have to remain the existing solution. We'll see what we can do, what things we can help make it work better on Meta. Some ideas include a new meta tag besides discussion to identify these, as well as better forms of filtering. We're going to be happy to try out a lot of different things, but there'll be a solution. Be it something we integrate into the main site, be it something that adapts Meta to a better way, be it ultimately a separate section of the site, there'll be a solution.
I will give one idea, though, that might help this site while we work on something more mechanically integrated - on Mathematics, they use a single thread for sandboxing, one that has a fixed number of answers. Rather than letting people just keep posting, you can only draft while there's an open slot for you to take. If the draft is "abandoned", it can be cycled out. This kind of strategy may help with some of the flaws that have been observed in the current sandbox strategy. Not all of them, but I hope it might be a useful direction to look at.