I think to a point yes we should, it encourages organisation and increases search engine hits, but where would the line be drawn? How would we define what element is important enough to get its own tag?
For example 'The Trojan War' would be a useful and popular tag, but perhaps 'Ajax's madness' would not.
On the other hand, I think it would be useful to have tags for generic elements. For instance, heaven or concepts-of-heaven or afterlife for a question on Valhalla. If someone wants to look up questions on a heavenly afterlife location, manual searches are not likely to be very productive - there's too many such places to search, and there's you can't search for an afterlife location if you don't know its name.
Basically I think tags should be beneficial for searching related questions, without being redundant with the basic search function.
I think early in a site, more tags is better. It's easy to create tag synonyms, but hard to remove them. Later, we can synonym the stuff that needs to get synonymed, if we decide we have too many small tags and want to put them under the same umbrella.