I would love to be able to exclude, for example, fighting games and platformers from my listing.

THIS. I never want to see racing, sports, horror, NSFW, etc. Though, not just genre. I would expand the idea to include filtering out cusomizable keywords by default as well (i.e., “abc”, “jigsaw”) and specific publishers.

I literally typed “negative filter” as a suggestion and this one popped up. Why most websites don’t have a feature like this is beyond me.