Let's start by touching on the problems that we hoped to solve with design-independent graduation, and then look at where we've come in regards to solving them.
Communities needed to worry more about just being awesome and not so much about where they stood in the midst of a rather arbitrary goal like graduation, or even just surviving as a small and relatively slow site.
The graduation of sites tended to get held up much longer than anyone was comfortable with due to demands on our designers.
Graduation reviews were a very subjective thing for the community team; there was a whole lot of 'you know it when you see it' and not very much 'science says this site is ready'.
Design-independent graduation either fixed, or heavily alleviated all of these problems.
Small sites no longer have to worry about the lights going off as long as they continue to produce helpful content at their own pace, and the site remains well cared for.
Sites with more momentum behind their topic know that they're looking at their next step once they reach 10 or more questions daily and consistently for a while, and there aren't any outstanding disputes on site scope or how moderation should play a role in keeping things going.
Graduation reviews are still somewhat subjective; an experienced community manager still needs to review a site prior to us elevating everyone's expectations. Were there problems finding leadership in the community? Is the site welcoming to new users and remaining relevant in its topic space? Do we have quality issues, like many answers just citing other sources without much else to add? Is the topic space still relevant, and will the site survive despite this? (did FooCMS cease development?)
These are just a few of the things that someone needs to check and possibly set a course correction to fix before we're ready to advance.
Design-independent graduation is always going to be a thing, it worked brilliantly and we're very happy to have it. Graduation is (at least for the foreseeable future) going to need some human involvement on our part; that's not going to change in the near future.
But you asked what's next! Let's get to that.
Since we're very happy to have any site that continues to help people get better at something as long as it remains well cared for, that whole "Beta" label becomes a little questionable.
We propose getting rid of "Beta" as soon as a site clears the Area 51 process successfully and goes public. Why? Because at that point, the site is (at a minimum) one that we'd love to have forever as long as folks take care of it while it grows at its own pace.
Sure, there's going to be at least one site that just won't make it even under the loose definition of what we'd consider a small viable site to be. But in the absence of new questions and moderation, I don't think it would come as a surprise to most if we intervened and closed it down, "Beta" or not.
We're open to any suggestions about what else could be next; you're welcome to leave a comment or start a new discussion based on this answer. We're extremely happy with how graduation has been working, but we want your thoughts too.
I can't promise that we'll implement any given suggestion, but we'd like to know what else you think should come next, and we're more than willing to talk about it.