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.  


> K.A. Bush, *[Classroom Notes: On an Application of the Mean Value Theorem](https://mathscinet.ams.org/leavingmsn?url=https://doi.org/10.2307/2307253).*  Amer. Math. Monthly  62  (1955), 577--578, [MR1529115](https://mathscinet.ams.org/mathscinet-getitem?mr=1529115).

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>  M.R. Spiegel, *[Mean Value Theorems and Taylor Series](http://www.jstor.org/stable/3029299)*.  Math. Mag.  29  (1956),  263--266, [MR1570819](https://mathscinet.ams.org/mathscinet-getitem?mr=1570819).

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>  D. Zeitlin, *[Classroom Notes: An Application of the Mean Value Theorem](https://doi.org/10.2307/2310172)*.  Amer. Math. Monthly  64  (1957), 427, [MR1529634](https://mathscinet.ams.org/mathscinet-getitem?mr=1529634).

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>C.L. Wang, *[Classroom Notes: Proof of the Mean Value Theorem](https://doi.org/10.2307/2308807)*.  Amer. Math. Monthly  65  (1958),  362--364, [MR1529949](https://mathscinet.ams.org/mathscinet-getitem?mr=1529949).

>(In this article, the derivation of MVT from Rolle's theorem by tilting one's head is presented in horrible analytic detail.)

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>J.P. Evans, *[Classroom Notes: Sequences Generated by Use of the Mean Value Theorem](https://doi.org/10.2307/2311591)*.  Amer. Math. Monthly  68  (1961),  365, [MR1531194](https://mathscinet.ams.org/mathscinet-getitem?mr=1531194).

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>L.C. Barrett, *Classroom Notes: Methods of Proving Mean Value Theorems*.  Amer. Math. Monthly  69  (1962), 50--52.

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>L.W. Cohen, *On being mean to the Mean Value Theorem.* Amer. Math. Monthly 74 (1967), 581-582.

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> L. Bers, *On avoiding the Mean Value Theorem.* Amer. Math. Monthly 74 (1967), 583.

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>H. Levi, *Classroom Notes: Integration, Anti-Differentiation and a Converse to the Mean Value Theorem*.  Amer. Math. Monthly  74  (1967), 585--586.

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>R.P. Boas Jr., *Classroom Notes: Lhospital's Rule Without Mean-Value Theorems*.  Amer. Math. Monthly  76  (1969), 1051--1053.

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>D.E. Sanderson,  *Classroom Notes: A Versatile Vector Mean Value Theorem*.  Amer. Math. Monthly  79  (1972),  381--383.

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

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>T.W. Tucker, *Rethinking Rigor in Calculus: The Role of the Mean Value Theorem.* Amer. Math. Monthly 104 (1997), 231--240.

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

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> J.J. Koliha, *Mean, Meaner, and the Meanest Mean Value Theorem.*  Amer. Math. Monthly 116 (2009), 356--361.

This list was compiled as follows: first I started with the five or so articles on MVT that I remembered, mostly from having appeared in the Monthly.  Then I did a MathSciNet search: "Anywhere=(mean value theorem)".  This gives 1589 matches.  Starting with the earliest papers, I looked quickly through the articles until I got tired.  My list contains all the articles that I spotted and thought to be of relevance to the question which were published before 1973.  This was about 25% of the 1589 matches.