Speeding up random number generation by parallelizing

I need to create many large numpy arrays (4e6, 100) with random numbers from a standard normal distribution, which I'm trying to speed up. I tried to generate different parts of the arrays using multiple cores but I'm not getting the expected speed improvements. Is there something I'm doing wrong, or am I wrong to expect speed improvements in this way?

from numpy.random import default_rng
from multiprocessing import Pool
from time import time


def rng_mp(rng):
    return rng.standard_normal((250000, 100))


if __name__ == '__main__':

    n_proc = 4
    rngs = [default_rng(n) for n in range(n_proc)]
    rng_all = default_rng(1)

    start = time()
    result = rng_all.standard_normal((int(1e6), 100))
    print(f'Single process: {time() - start:.3f} seconds')

    start = time()
    with Pool(processes=n_proc) as p:
        result = p.map_async(rng_mp, rngs).get()
    print(f'MP: {time() - start:.3f} seconds')

    # Single process: 1.114 seconds
    # MP: 2.634 seconds