So I'm just curious why they don't exist, was there ever a conscious decision to not create any character tags for Game of Thrones?
Because nobody has made them so far. The default position for any tag is not to have it, up until someone adds it to a question, so it's less "a conscious decision to not create any GoT character tags" and more "no conscious decision to create any GoT character tags". In the beginning, it wouldn't have made much sense to have character tags when there weren't enough questions specifically about any character. Now, with so many game-of-thrones questions on the site (and with the knowledge of which characters survive to the end and which ones don't last long enough to be important), it might make sense to use some GoT character tags, but nobody has gone ahead to start editing them into older questions.
Character tags are controversial in general. Some users have strong feelings against character tags - any character tags - and consensus on them has been far from clear over the years and meta posts. (I'm guessing that this very meta question of yours is likely to receive a lot of downvotes.) That gives a clear reason why some users haven't added any GoT character tags - because they don't like character tags at all. Maybe other users haven't added them because they feared complaints or drama around them. Or maybe it's just as simple as they couldn't be bothered.