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If all you want to do is to generate a texture by looping over all pixels in sequence, then yes, you can use a RNG. But in many use cases you need to evaluate a noise function at an arbitrary (x, y) position (or (x, y, z) or even higher dimension) which means you need to hash the coordinates to get the pseudorandomness you want.

A desirable property for this is to be able to generate only some part of the terrain, but if you're using a seeded PRNG then you have to generate the same bits at a time. You could solve this with chunking, but it's not trivial.

Indeed like others mentioned, it's about being able to generate terrain chunks starting from anywhere in the world.

A random number generator using the same seed would still have to follow the same steps for all users, meaning generating the world from the origin.

Correct, you can use an RNG. It's no coincidence that many RNGs and hashes (and, for that matter, ciphers) have similar constructions.