Chromaticism doesn't defy traditional notions of melody. For example, Purcell's got all kinds of chromatic noodles in his melodies and people love to sing them.
What's melodically defiant is how disjunct that fugue subject is-- it keeps leaping around different registers with two-note sighing motives. In that sense it sounds like what a string instrument should be doing in the inner voices to fill out the harmony. Instead, it's presented unaccompanied at the beginning of the fugue because... that's how fugues typically work.
The reason it works is because the people who play and listen to Bach understand fugal forms and textures. They know that an unaccompanied fugal subject often has rhythmic and melodic holes in it precisely to leave silence that gets filled in later with the arrival of two or more additional melodies.
Lest you think you're too uninformed to hear any of this-- listen to Conlon Nancarrow's Study No.36 for Player Piano[1]. It's a four-part canon where, like Bach's fugue, Nancarrow leaves rhythmic and melodic space for the other voices to fill in as they enter. Except Nancarrow tweaks the tempo of each voice so that they move with a ratio of tempos that equals 17/18/19/20. If the result sounds unhinged to you, then congratulations-- you understand and can hear the basic musical premises that underpin Baroque period fugal forms.