then it's Kolmogorov complexity is also extremely low.
Look if you have a well enough hash function, it output should be near the Shannon limit and hardly compressible, and ideally contain as much entropy as it has bits. But you can feed in just a single bit or the entire knowledge of humanity, in the end you're going to get a fixed amount of bits, and entropy near of that, and if you throw any form of lossless compression at it, it will hardly compress.
But quantum mechanics tells us, that information cannot be destroyed. So when you feed it more bits, than it emits, then its mostly the entropy of the information you feed in, that you get out of the hash. But if you feed it just a single bit, the additional entropy comes from the computational process.
I know, this is now getting really philosophical, but here's something to ponder on: How would you implement a hash function for a reversible computing architecture?