For the same reason we lack SA3 Unidivision.
So when it comes down to votes, I say either axe, or (extreme case) freestyle. But preferably the former.
(For the record, my S3DB scores don't use special stages.)
On a semi-related though unrelated note, why are there ring stats for S3DB Act 3's when, on similar boss-only levels in other games, there aren't?