Fun project. FYI, on my machine:

    In [1]: X = randn(10000,100)
    
    In [2]: timeit apply_along_axis(np.mean, 0, X)
    100 loops, best of 3: 7.91 ms per loop
    
    In [3]: timeit X.mean(axis=0)
    1000 loops, best of 3: 1.21 ms per loop