One of the more common changes across platforms in recent years has been a move to make it easier to filter out content you don't like. While that is good in some ways, it also leads to extremism by reinforcing all of your current opinions while filtering out all competing views. Tags would allow people to say 'I want posts with this tag, but not any with that tag' and therefore allow people to filter content they care about very easily, but would lead to bubbles (like tumblr's SJWs) very easily. Reddit has a half measure of grouping things into basically only one tag, meaning it may consist of other tags as well, but there's no way to know. This creates a lesser bubbling effect as it's much harder to ignore specific ideas altogether. Some gaming posts may contain ideas about gay marriage, some videos may contain content from the political party you don't like. It allows just enough content to filter through so that it is not entirely avoidable, unless you unsubscribe to that entire subreddit. There certainly are those who specifically unsubscribe from subreddits to avoid certain content, but they also miss out on a lot of the content reddit has to offer.
For this reason I'd recommend going with boards rather than tags. Maybe a board can have multiple tags, but posts shouldn't?