Your initial post did not say that you can have both, and your opening paragraph explicitly states that you think these two are in direct conflict. When I made this post I did not see your post where you elucidated that in your proposal they would not be mutually exclusive.
If the system works in this way, then I've got no strong philosophical objection to it. My only suggestion would be to have "neither" as an option in addition to "both", since I think trashgames would pretty comfortably fit in that category.
At this point my real critique would be that I don't know how effective it would be at addressing the problem you're trying to address. The artgames tag already exists, so if the problem is that you're having a hard time finding art games, then how would adding a different way to tag your game as an artgame fix the problem that people aren't tagging their artgames as artgames?
And what about the backlog? The majority of content on any free-to-upload platform is going to be hit-and-run uploads, stuff that the original creators are no longer maintaining, so probably the vast majority of games released before the new feature is introduced will never be updated to use it.
I'm having a hard time understanding what the problem even is that you're trying to address.