One very likely reason for the odd split fret is as a customisation to fine-tune a particular note of the scale.

If you play in double C tuning: gCGCD, the note on string 1, fret 2, would be an E, making the major third of a C chord. In equal temperament this is much sharper than a "just", or harmonic third, which would tend to sound smoother in a chord. By having a split fret, that one note could be "fine-tuned" without affecting any others. A big drawback though is that it would only work in the one key.

However, if you were playing with an instrument that was just-tuned, you'd almost certainly hear the difference on that one note. I recently ran into exactly that problem recording a song with banjo and harmonica. Harmonicas are often tuned in just intonation because chords sound smoother (and as there are only really two of them on a diatonic harp, that doesn't create too many problems)

I've seen pictures of guitars (and occasionally bouzoukis) with split frets and/or extra frets to accomodate some pretty wild and wonderful tuning schemes, but never a banjo. A fretless banjo would allow you to play any note as sharp or flat as you like, but would really mess with your chords.