To start with a bit of history, this site was actually added to the queue for graduation in roughly October/November of 2013 (less than a year after private beta!). At the time there was no procedure for graduating beta sites without creating a custom site design, and the design team was rather understaffed with several other sites ahead of us, so we had to wait for them to do something. A couple years later in 2015, a procedure was created for graduating sites independent of designs, and this happened fairly quickly here after the new policy was put in place. If you read that post, you will see that we still expected to wait a few months for a site design, and that in particular the reputation thresholds for privileges would remain in place until the new design arrived (most other changes happened immediately). I'm not sure exactly what the reason was for coupling only these two aspects of graduation (some information can be found at Feedback Requested: Design-Independent Graduation and in other MSE posts and meta sites graduating at the same time but there does not seem to be a perfectly clear answer, and even at the time among the community team not everyone agreed), but at the time no one here was complaining much about it since this was a clear improvement over the previous policy.
It's now been well over a year since that announcement. Collectively, we've been waiting over 3 years for a site design (and the corresponding threshold increases), and I've seen no updates recently to suggest that this is any more likely to happen now than it was 3 years ago when we were first contacted by someone in the design team. Meanwhile multiple sites which did not even exist at that time have had designs made. Every other site which was in the queue with us has long-since been designed. Of the newer sites which have been graduated without a design, Code Golf has had the longest wait, and they haven't even been waiting a full year yet. By far we're the most extreme case in the network, and during that 3 year period numerous other changes have happened on this site. When design-independent graduation was first implemented it was never intended to be a long-term state like it has been here, and in such a long-term case it seems to no longer make sense to tie other changes to the design.
To be perfectly honest, I actually don't care very much about the site's design itself (though I certainly can't speak for everyone on this and I think it would not be unreasonable for other users here to be upset about this situation). It would be nice to have a good design, but I understand why it's particularly difficult to come up with something satisfactory for this site. There are at least 3 different groups you have to satisfy with the design. First, questions here are divided, with many questions about popular mainstream series, but still a fairly significant fraction in the long tail of questions on works which few are knowledgeable about. Some users here come only for the big name series like Naruto and Dragon Ball, which obviously tend to attract the most traffic and answers. Others (including me) come almost exclusively for the smaller works, and at least personally I'd argue that this is where we've really improved Q&A coverage versus other sites on the network with overlapping scope such as Science Fiction & Fantasy and Movies & TV. Between these two there is some common ground, but not much. There's also the broader SE community who can end up here in a few ways, and as such we need something at least a bit unique and clearly anime/manga-themed. The strategy used on Arqade and Movies was to have a classic look, but I don't think that would work at all here. Other major anime/manga themed sites like MyAnimeList and Anime News Network have fairly bland designs, but fill in the space with a lot of images of specific works and advertisements, but that wouldn't really work either. My answer here is basically about the same issue, and I don't think views on this have changed since then.
So I'm not really sure what a good design would look like. It also doesn't seem like the kind of thing that the design team's experience would be likely to help with, because the problems here are intrinsically related to our site's content and scope, not artistic issues, and I doubt anyone on the design team is specifically an expert on our site's content. The one thing I think almost everyone can agree on is that a bad design, which overly emphasizes only a small subset of the community here, would end up worse than our existing look (just imagine if it's designed primarily based on a genre/work that you actively dislike). The current look isn't anything special, but it's perfectly functional and neutral. I don't think creating a design for this site is an impossible problem, but it isn't one that I know the solution to, and the design team seems to have come to the same conclusion. As such (and as they've had plenty of other work to prioritize ahead of us, especially considering the answer here which suggests that many more sites may "graduate" to a similar state as ours, allowing the design team to backlog our design effectively indefinitely) it hasn't happened and doesn't seem likely to happen any time soon.
However, if graduation without a design is going to be the de facto standard on this site for years (possibly even forever for all we know at this point), it does not seem reasonable to me to keep the rep thresholds at the low levels of a beta site. Hence, I am requesting that the rep levels be increased to the standard graduated site levels here now, regardless of when (or even if) a design is made for the site. Most importantly, editing would be reserved for 2k users and close voting for 3k users, rather than 1k and 500 respectively on the current site.
I argued almost 3 years ago that we needed more high-rep users to be ready to graduate. In that time, the numbers have changed drastically; now I think we have the opposite problem where we have too many users at the low beta-level rep thresholds. That's not to say that I think any users in particular are doing a bad job, but higher rep users could easily handle everything that comes up, and will on average probably have a better understanding of site policies and what constitutes high-quality content here. I'm also worried that the lower rep thresholds discourage extended participation on the site. Certainly this happened for me, so I'm speaking partly from first-hand experience. Roughly when I hit 10k rep, I decided to stop answering questions which I thought others on the site could handle without me. Without higher rep targets to hit, and with few questions that only I knew the answer to (and many newer users who weren't around since day 1 finding it difficult to gain rep), it was rare to find a situation where I cared to answer. Actually many of the highest rep users on the site are not posting that regularly now, so I don't think I'm alone in this (though this is a separate issue which probably deserves its own meta post). In my case you could partly attribute this to other factors but I think in general if the rep thresholds were higher, we'd overall see more Q&A participation from all users.
I guess this change is probably at least somewhat controversial. Having 20k rep myself I'd be mostly unaffected, but many mid-level rep users would probably be somewhat upset to see their long-held privileges removed suddenly, especially without a site design. However personally I'm convinced that, for the long-term health of this site, this needs to happen eventually regardless of whether we ever get a design, and if it's going to happen anyway it might as well happen now.