While reading the inevitable-at-this-time-of-year posts complaining about how terrible the Hugo Awards are and how some categories shouldn't exist at all (different people have different and mutually contradictory groups of "kill these categories" on their lists), but also considering how difficult it is to actually remove a category once it starts unless it is an utter and obvious failure (Best Original Artwork being the last one; it seems like such a good idea, but in practice it simply doesn't work), I came up with a new idea that would give the membership a chance to weigh in on the subject.
The proposal: Require Every Hugo Award Category to re-qualify every five years. And I mean every category, even Best Novel. Divide the list into five roughly-equal-sized classes (and require that any new categories be assigned to a class when they are created), and submit that year's class of categories to the membership for an up-or-down vote. If a category doesn't get a majority (more yes than no votes) in favor of it, the following year's Business Meeting would be required to craft a proposal to eliminate the category (possibly merging it with "adjacent" categories if that's practical), and if the BM is unable to decide upon a merger proposal, the simple question "Shall [X] be removed?" would be submitted to the following year's members for ratification.
[Update: per comments below, substitute your desired interval; five was just an arbitrary starting number. For example, you could require only one category per year come up for re-ratification, which would currently take sixteen years to do the entire cycle, and any new category would "get in line" and be up for re-ratification seventeen years later. That might be a little slow, though.]
Complicated? Yes. Slow? Yep; it would take three years to kill a category by this process, and you'd only get one "referendum" shot every five years. But it would give every member, including the basic, non-attending (currently called "supporting") member, a chance to weigh in whether a category has outlived its time or not. It would furthermore give a voice to the non-attending members currently denied to them.
[Update: Linda Deneroff's comment reminded me that if we allowed at-con voting (which I would want to do, in parallel with site selection), it wouldn't be practical for the same Business Meeting as the year the voters tried to kill a category to craft an implementation proposal, and thus the entire cycle time would be four years, not three.]
You might be surprised, given that I've attended every WSFS Business Meeting since 1989 and chaired it several times (in four different countries, a record unmatched by anyone, I think), that I would favor any proposal that took away any part of the tiny bit of power that the WSFS Business Meeting has. However, I think that WSFS is only as good as its own perceived legitimacy, and there are a lot of people (some of them with what I think are plausible arguments) who bitterly complain about how the process is dominated by a relatively small group of what they consider "insiders" (the Evil SMOFS) who know the process very well and who tend to vote down any significant change because they're hidebound conservatives. While the perception that the Evil SMOFS are a single monolithic bloc that reject all changes is in fact ludicrous, I understand how some people might feel this way about it.
Personally, when I came to Worldcon and got frustrated because I didn't get the things I wanted, my reaction was to learn the rules and do my best to change things from within, and to a great extent, I succeeded; however, I'm sure there are others who would look at my path and just tell me that I've become part of the problem and that I should get out of the way and let Real Fans have their way. Unfortunately, my opinion is that a bunch of those people are really saying, "You should keep running things because we're not willing to do the work, but you should change everything to suit us because we said so." Well, maybe the barriers to entry are a little difficult, I think it wouldn't hurt to lower them a bit. And I also think that it would do more good for WSFS if the non-attending members had a few more voting rights than just the Hugo Awards; if nothing else, it would work against those people who characterize the current state as "you have to pay to vote" because they brush aside the fact that voting is for members only and that WSFS has membership dues as some sort of sham.