I don't see why tagging is a bad thing. It essentially allows sub-Reddits to still exist while providing people an opportunity to submit content to multiple relevant topics.
Subreddits allow curation by group and group-specific discussions instead of classification en masse. It also allows private (you have to apply for membership/not publicly viewable) groups and community-specific discussions.
There are different subreddits for 'programming', 'compsci', and 'python' for example. For a link relevant to all three it isn't always desirable to have a giant group discussion. Similarly, there are subreddits for 'science', 'askscience', 'softscience', 'sciencepolicy', etc. All which might have articles that, if reddit had tagging, would be tagged for science. And there's like 50 different subreddits about smoking weed. All serving different communities. Or maybe they just forgot where the pot smoking subreddit was so they keep creating new ones. The point is, tags would be all inclusive.
Crossposting isn't really a problem and is often desired. You can see all discussions related to a link by clicking on the "other discussions" tab when viewing the comments.
I completely agree that the group-specific discussion is pretty useful.
I slightly disagree about crossposting not being a problem. On major issues that populate multiple Reddits, it gets cumbersome to see the same headline used on multiple Reddits, such as say Reddit.com/WorldNews/News. It's the only way to get around the lack of a tagging system. How does one choose which discussion to follow? It's easier for me to look at comments in one 'thread' about one incident or specific story rather than four or more, especially when the same arguments/observations are made.
On AskReddit, people post a lot of questions that should be in other subreddits but it's still upvoted anyway. Some do this because the applicable subreddit's aren't discoverable and so they don't know they exist. Others do it because AskReddit has such a vast number of subscribers more than the related sub-reddits.
With tagging, it's also easier to discover new communities/tags. How do I discover a new Reddit outside of hearing some person in the comments talk about something? With tagging it's clear as day.
