White noise is random, so it's incompressible by definition. By JPG or by any other method no matter how clever.
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.
What you're saying is only true for lossless compression, if you're fine discarding data you can compress anything. Try it yourself:
Result is ~380k smaller and doesn't look much different at 100%.