What you're saying is only true for lossless compression, if you're fine discarding data you can compress anything. Try it yourself:

    magick -size 512x512 xc:gray +noise Random noise.png
    magick noise.png -interlace Plane -quality 75 compressed_noise.jpg

Result is ~380k smaller and doesn't look much different at 100%.

I have a very peculiar coin. With 1% probability it turns up heads and with 99% probability it turns up tails.

A string of flips is random, but it's very compressible.

In any case, my point was that reality ain't uniformly random. And not only that: pretty much anything you can point your camera at shares enough similarity in their distribution that we pretty much have universal compression algorithms for real world data.