The purpose of this answer (which I would make CW even if the question weren't) is to collect references to scholarly articles on MVT and its role in introductory calculus courses.  Most of these articles have some real mathematical content: e.g. they discuss logical implications between different forms of MVT.  Certainly they are written by people who have thought deeply and in novel ways about this result -- i.e., by mathematicians.  


>[1] L.W. Cohen, *On being mean to the Mean Value Theorem.* American Mathematical Monthly 74 (1967), 581-582.

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>[2] L. Bers, *On avoiding the Mean Value Theorem.* American Mathematical Monthly 74 (1967), 583.

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>[3] R.P. Boas *Who needs these mean-value theorems anyway?* Two-Year College Math. J. 12 (1981), 178--181.  

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>[4] T.W. Tucker, *Rethinking Rigor in Calculus: The Role of the Mean Value Theorem.* American Mathematical Monthly 104 (1997), 231--240.

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>[5] H. Swann, *Commentary on Rethinking Rigor in Calculus: The Role of the Mean Value Theorem.* American Mathematical Monthly 104 (1997), 241--245.

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>[6] J.J. Koliha, *Mean, Meaner, and the Meanest Mean Value Theorem.*  American Mathematical Monthly 116 (2009), 356--361.

This represents less than 10% of the available literature, I believe.  If you want to add references, please feel free.  (Note that they are ordered chronologically rather than alphabetically.)  If you would like to supplement the references with free links to the actual papers, that would be fantastic.