http://wpt3ch.com/wp-content/uploads/2016/06/moving-the-lower-case-c-up-above-type-in-the-last-name-mcneil-english-stackexchange-com.jpg
I believe this is because the name element (now) usually expressed "Mc" is actually an abbreviation for "Mac"; at one time, superscript (often with an underline or under dots) was a common way of writing abbreviations without resort to an apostrophe. This is preserved in the symbol № for "number".

You can see an example of this in the signature on the letter below, abbreviating "Nathaniel" (from Wikimedia Commons):

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Writing Mc as MC therefore preserves the original, "true" form of the name in a way that Mc does not (as it does not indicate the abbreviation).

There is also a discussion here about the aesthetic and legibility benefits of the superscript c, for more formal type-setting.

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