Admin only tags, plus required tags?

Yes, it IS now possible (since version 2.0). You can see the discussion here:

If you have enabled tags on your site, then you have a category setting that allows you to determine how many tags are required as a minimum:

We use the term topic to mean the conversation, beginning with the first post. So the topic is the original post and all the subsequent posts in the conversation. You are not able to tag the posts individually, but you can add the tag to the topic.

If a post within that topic is different or unrelated, and therefore requires a different tag, you can always select it and convert it into a NEW topic or merge it with another relevant one.

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