Even Strassen can be overly expensive for reasonably sized matrices. Almost all matrix multiplication algorithms have a threshold only beyond which do they use Strassen.
Although apparently that threshold can be lowered (http://jianyuhuang.com/papers/sc16.pdf), but even then it's a matrix that's several hundred columns by several hundred rows large.
Some CS classes explicitly use Strassen to teach the realities of asymptotic vs wall-clock time complexity, challenging students to come up with a hybrid matrix multiplication algorithm that performs the fastest and switches at the best thresholds of matrix size.
Although apparently that threshold can be lowered (http://jianyuhuang.com/papers/sc16.pdf), but even then it's a matrix that's several hundred columns by several hundred rows large.
Some CS classes explicitly use Strassen to teach the realities of asymptotic vs wall-clock time complexity, challenging students to come up with a hybrid matrix multiplication algorithm that performs the fastest and switches at the best thresholds of matrix size.