Please visit a homepage for a “dedicated” site, and attempt to imagine how you would recreate that environment for a “sub” community on an existing Stack Exchange site.
And now you have begged the question: your statement assumes that it is necessary to "recreate that environment" in order for something to happen.
You've missed the point: we do not want to recreate that environment.
We don't want sub-communities to have a tag page that looked like its own site. We don't want sub-communities to have their own metas with their own meta-questions. We don't want sub-communities to have their own moderators.
In short, we don't want sub-communities to pretend that other sub-communities do not exist.
We want sub-communities to feed off of each other. We want them to learn from one another. We want them to all be programmers, gamers, etc all together, as part of a single unified whole. Not separate C++ programmers and Appcelerator developers, WoW players and Skyrim players, but programmers and gamers.
Here, we are one.
You ask this question, but you've never answered or justified its inverse: why do you believe that a particular community needs a dedicated site? Why do Appcelerator developers need to filter out every question that isn't about Appcelerator? Why do Appcelerator developers need their own moderators to control just their questions and answers? And so forth.
It depends on the communities in question. There is no single standard.
There was a lively discussion about this subject when the Magic: The Gathering proposal was absorbed into Board & Card Games. Most of that discussion seems to have been deleted (for some reason) along with the MtG proposal itself. Some of that discussion still exists, though.
But let's cut to the real issue: this is merely a continuation of the discussion from here, which itself is a continuation of your desire to see a dedicated Appcelerator site on Stack Exchange. So let's look at that in the context of your question here; it makes for an effective demonstration.
We don't allow SE sites to have total overlap with Stack Overflow. Ever. The whole Unix&Linux vs. Ask Ubuntu thing would not happen with SO. If a proposed SE site's questions would all be legitimate on SO, then we want those questions on SO.
The reason for this is very simple, and it is exemplified by Appcelerator: programming isn't just one thing.
Now, before I continue, I'm not a web developer. I don't really have anything beyond the most basic familiarity with web technologies. So I freely admit that I may be wrong in my assessment of Appcelerator.
There's also a desktop interface which includes PHP, Python, and other technologies and languages. Again, there will be some problems that are API specific, and some problems that any Python expert could help you with.
By segregating yourselves off in your own little corner, you have also segregated yourselves off from many experts who might sometimes be able to help you.
Now, you could say that you'll just ask those general questions over on Stack Overflow. But if you're going to do that... why not just move everything over there? Not to mention, that doesn't solve the problem; sometimes, you think something is an API-specific problem when it's really just doing something stupid with the language.
Different sites act as a hard barrier to community participation. Questions asked on one site are invisible on another.
Programming is special in that it has a lot of overlap. Most programmers don't specialize to the extent of being totally ignorant of other technologies. Many programmers have dabbled in other tech. If someone who's a frequent visitor to SO wants to start some Appcelerator development and needs questions answered, he's going to find it much easier to do that if he doesn't have to go to another site to get those questions answered. So here again, cross-talk serves to enhance a community, not weaken it.
The cross-talk that happens is one of the most valuable aspects of Stack Overflow.
But I would say that the benefits of cross-talk far exceed the downsides. And moderators can help alleviate the downsides.
What is the benefit from having a dedicated site?
One interesting thing that came up often in the Magic: The Gathering discussion was the notion of identity. Many people suggested that forumites and such would only come to an SE site to ask MtG questions if it were a dedicated MtG site. That they would not find it acceptable to spend time on a site that catered generally to card games. That they see themselves as Magic: The Gathering players, not gamers in general.
Personally, I don't get this isolationist mentality. Initially it might seem off-putting, but once you get there, it's nothing terrible. There are many web developers who wouldn't have the first clue about things like C++. And yet, they don't mind Stack Overflow having C++ questions. If the community tells its members to use the site, then the site will be used.
Is it possible that some potential users of SO don't use it because it's not dedicated solely to their field or technology or whatever? Possibly. But there are anecdotes of people branching out of their field because of SO. Indeed, I've seen users who answer questions in one field and ask questions in a different one.
One technology's expert is another technology's neophyte.
The benefits of cross-talk are why we have the "no duplication of Stack Overflow" rule on Area 51. Among programmers, "sub-communities" are far more fluid and dynamic, with intermingling and mixing to the point that it becomes a harmonious whole.
Also, I would take issue with this:
Clearly Stack Exchange believes there's value to having dedicated community sites
No; Stack Exchange believes there's value in getting people's questions answered. Dedicated sites are created in order to serve that need: answering questions. If a site already exists where that question can be answered, then creating a dedicated site for it serves little purpose.