A search result for Mean Value Theorem gives us 2715 results, and results on the page are like ones I think we can include in the tag. The theorem is an important result in calculus, and questions relating to its applications, proofs. I think it would be useful if could have the tag, as it can group the related questions, and create a reservoir of such questions that would be good to look at, users like me can favorite the tag which will bring us new interesting questions on the subject.
I disagree. A reservoir of such questions already exists here, anyone can look at it as much as they like (note that I use quotation marks to pick up the exact phrase: 938 results). Out of these, only 341 are questions involving "mean value theorem": the term is more likely to appear in an answer than in question body. Which means in most cases the person asking the question does not know that the solution will involve the mean value theorem, and consequently will not tag the question with it.
If we start creating tags for individual theorems, then there's also Intermediate Value Theorem, Fundamental Theorem of Calculus, Fubini's Theorem, and so on and on and on and on.
Lastly, this is not a feature-request, because you are not asking for a new feature to be added to the site. (The tagging feature already exists). As long as we are on the subject of using tags properly...