In his treatise Versuch einer geordneten Theorie der Tonsezkunst (1817) he talks about categorization of what he refers to as "four-fold chords" (which we know as "seventh chords") saying this (English translation by James F. Gottfried Weber was one of the earliest writers to use what we would recognize as "modern" chord symbols in harmonic analysis (as opposed to the more traditional figured bass or Roman Numerals).
The answer is that even though a C major seventh chord would fit more "naturally" in the C major scale, the dominant chord is much more fundamental to our conception of harmony (for example, in the C major scale, G7 is a very important chord because of the tonic-dominant relationship). So why does the dominant seventh get the "default" symbol of C7 whereas we have to qualify the others as CMaj7, CMin7, etc.? Another way of looking at the question is this: we have a number of seventh chords, dominant, major, minor, diminished, and so on.
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