Chris,
I think that there is broad consensus that the category problem is one of the worst problems with Mediawiki software and that all projects suffer major harm in many ways because of it. I do not think that there is anyone who defends the current system except to say that it is what we have now and fixing the problem is a major undertaking which will take a lot of time for many developers.
I do not think GLAM could really solve this problem, but it would be nice for GLAM to support the development of community infrastructure wherein community members get more opportunity to express concerns to developers. Another problem is that while many surveys show that the community supports WMF efforts to do software development, there is a huge amount of bad blood between developers and anyone who participates in the community processes around developing. Just recently in IRC meetings and other efforts there have been complaints about echo, for example. I am sure that you all saw that you have a notification box by your names now, but when developers rolled this out, they also removed the orange "You have new messages" box that used to appear. This caused problems, like for example for IP users who really need an orange alert to know that they are doing something wrong, and for other people who just do not know to look at the new box. I am in favor of change but developers can be heavy-handed, and for them to do work they need community support.
The way things ought to be is that there should be a layman discussion space for projects which gives explanations of what is proposed and where we are in the process of fixing things. This would link to developer discussions. Chris, in answer to your question about where to find more info, I think that such a place does not exist and that the archives are mostly a mess. This category problem is a big issue that lots of people notice but no one knows where to put their energy. There are other big problems, but from my perspective, the category issue is one of the biggest. I do not understand Wikidata but it seems to me that the solution should come from there, because I also think that categories should transcend each language and by default be uniform cross-Wikipedia.
It would be great and empowering for women if any user could immediately, for example, get a list of women authors or X demographic who work in Y field. It seems hateful to some people to have categories for "women writers", but having tags for "women" and tags for "writers" is exactly analogous from the Wikipedians' perspective but not hateful.
If anyone wanted to organize an effort to schedule development then I think it would be well-received by the community, external protesting organizations, the WMF, the developers, all organizations like GLAM, and all other stakeholders.
yours,