First off, sorry for taking so long to reply to this... I know it's not July anymore. For those familiar with the Eisenhower matrix, I classified this as important, but made the mistake of allowing it to be pushed back again and again for urgent pop-up stuff. Getting to it, then...
Short answer: CraftCMS SE is doing just fine.
When do the SE powers that be recommend this stack becomes official and not a beta? It seems there's no "formal" process but looking at the numbers, we have to be close.
As the other answer here notes, we on the community team no longer think of beta sites as being merely "works in progress" or otherwise incomplete, as of about two years ago. We've failed to come up with better terminology to replace "beta" and "graduated" with—although we should—so it's no wonder that the "beta sites need to make progress" myth continues to persist. Improving this is on our agenda, but it seems there's always something more visibly broken or immediately pressing to work on (see previous comment about Eisenhower matrix).
We're happy to consider CraftCMS one of our numerous "small-and-healthy" communities, just the way it is. You're already fully "official", and you shouldn't feel like you have to reach graduated status on our account. Nothing bad will happen to you if you stay right where you are. "Small-and-healthy" is a perfectly good permanent state.
As for process, here's what we're doing these days: In our opinion on the community team, the number of new questions a site receives per day is the most important characteristic for determining whether a community is ready for graduation. (There's no clear causal reason for this, but we noticed a strong correlation.) As a general rule of thumb, we seriously consider graduation when a site starts getting ten new questions every day, but not before. For a couple years now, you've been hovering steadily in the 6-8 range.
When that bar is reached, we'll do a final "sanity check" review. Just to make sure misguided people weren't artificially inflating the daily question rate by posting a ton of junk that immediately got closed or unanswered, and that the site has a strong core of expert users.
According to Area 51, we aren't much different than when EE's stack launched. We have better numbers in all categories except for avid users and answer ratio (and those 2 are too close to call).
The ExpressionEngine site graduated before we came up with the current system, when decisions were based much more on individual opinions, random memories, and probably the team's lunch schedule. The vagaries of that old system are what drove me to push for the new, more quantitative method.
We no longer assign much importance to most of the numbers shown on Area 51 proposal pages, such as "avid user" count or answer ratio. They're not useless to look at—I would consider "10% answered" a red flag during sanity check—but all in all, the signal they provide is limited.
The reason I ask is if you spend any time on other SE's, you get the feeling that Magento, WordPress, and EE are established platforms just by their look and feel and branding, and Craft is not.
I understand where you're coming from with this. I've been unhappy with the sparseness and wide distribution of our beta design for years. Unfortunately, graduation no longer comes with an immediate design, although it is still a necessary step along the way. Even if you graduated today, a redesign would be months away. I'm sorry to say we simply don't have the resources to create full site designs quickly right now.
And to top it off, our numbers are even better than Joomla's beta, an "established" CMS with a bigger percentage of users than EE and Craft combined—and with more time in beta. You'd think they'd be blowing us away in usage just with their marketshare. Isn't this what makes a great stack? The community?
You can also make the argument that having an "official" Stack "legitimizes" the CMS too, thus further garnering usage. (Well maybe in Joomla's case, the old Yogi Berra quote "Nobody goes there anymore, it's too crowded." is correct - ha!)
From a marketing perspective, that would really be awesome for that to happen with the release of Craft 3.
We don't consider the nature of topics when we look at graduation decisions. Our only concern is the health of the specific Stack Exchange site in question. We're here to serve the community we have, not any third party, whether that's Pixel & Tonic, the Joomla! Project, the Raspberry Pi Foundation or Apple Inc. Most of our sites are about abstract concepts, and don't even have an associated third party to consider, going from Stack Overflow all the way to the new Vegetarianism/Veganism.