Two reasons: first, the matrix multiply algorithms with exponents less than three do not have the same numerical stability properties, which can introduce subtle bugs into software that was developed with the expectation of a "usual" O(n^3) multiplication being used. This makes it unsuitable for use in a general-purpose library.

Second, although algorithms with smaller exponents exist, there is more to high-performance than asymptotic complexity. In particular, the constant factors associated with these "fast" algorithms are typically large enough that there is no benefit to using them for "reasonable" matrix sizes.