Metal songs using locrian come to mind, like Metallica’s “Sad But True.” Theoretically, locrian should be minor, or diminished if you count that separately. In practice, there’s just no tonic triad, and the closest thing is a plain power chord, omitting the third and using the perfect fifth. The power chord works because it outlines the prominent harmonics of the 8vb from root, to manufacture a phantom fundamental. So the theoretical locrian progressions like io-bII-bV-io can be approximated in play as 1-bII-bV-1 and it has nowhere to fit in your categorization.