You could use world position (or just some non-uniform sampling) to offset the UVs and get a similar effect, no? Is hex significant or is it just one of any number of ways to break up the uniformity?

In practice, yes, it's very common to use a shader to sample the texture with some rotation and noise. Most games have a shader level implementation to address this, and we've done that for a decade at least.

See: https://iquilezles.org/articles/texture repetition/ for a good breakdown on some techniques.

the URL should have been https://iquilezles.org/articles/texturerepetition but this is indeed a great resource