If I understand you correctly, I would say this is an interesting point you are making. Not sure if it is doable, or how it could be facilitated, but nevertheless an interesting point that should be pondered.
Graphic design are universes more than just making business cards and ads for toothbrushes. I venture the statement: design is the intermediary between information and understanding. It does not matter what information (though toothbrushes are decidedly on the boring side).
Graphic design are in bed, spooning with Art. They are two different individuals but intimately connected. Often, the same people create both art and graphic design, so they can be difficult to differentiate. There is a barrier in me personally, to call some of the stuff i do art. It is not quite graphic design either, but I find it hard to accept it as art. However, technically, objectively, that is what it is (it may not be good art). You will never find me in an art forum.
Personally I would like to see GD go in the direction of less digital-tool-fixation ("tell me how to do this in Photoshop") to a broader view, more ideas, history, methodology. I would love to see more people splattered with paint here; more of the eclectic and slightly obscure. Cartoons, children's books, scientific illustration, data visualisation, book production, doodles, various print-on-demand solutions and objects, charcoal, art prints, fabric design, signage, sketching, reconstructive illustrations, lettering, architectural visuals, DIY bookbinding, placards for protest marches, metal, leather, plastic, weaving, stencils, streetart, graffiti, low-tech photography ... anything, really. More, basically.
My interpretation of how SE should work, is basically like a scientific paper: someone asks a question, you give an answer that you can verify and exemplify, and then you are welcome to disagree with what you might have described previously as best practice. or common solutions. So there is room for personal opinions and reasons for personal opinions. Sheer opinionating, however is rarely useful, interesting or fruitful. The net is full of forums with endless, badly worded dis/agreements with little substance and reasoning.
I would therefore welcome personal opinions on stuff, as long as they are put into context. And that could give a little leeway to purely aesthetic appreciation.
SO, I agree with you there, is a monster in many ways. SO is so run down with thousands of questions every day, parts of the site will inevitably go feral. And there is a fundamental difference in programming versus design. A programming problem have a finite number of solution. Graphic design do not. Or at least; a programming problem have a smaller number of finite solutions that graphic design.
I have briefly popped into some of the other SE sites, and it is clear to me that there are a good deal of topics not at all suited for SE. GD, I believe, have earned the right to its own existence. it is not perfect, I wish for more room to manoeuvre. But I do believe that the community-run model is the best option there is. The day I loose the faith in that, I will find somewhere else to hang out.
The image of the tags that irks you, is the Meta-tags required, and the fact that Meta is limited in tags. It threw me first time, but I think it somehow makes sense: Meta is the place where the site is discussed, and these tags I imagine is very useful for the moderators that operate across the entire Stack exchange site. I think they divide the tags between them. I am more concerned about the willy-nilly tagging in the main site, and choose not to get my knickers in a twist over Meta.