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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