If you have 300 bits of shuffling entropy, you have a lot of potential assignments that can never happen because you won't test them before the universe runs out. No matter how you pick them.

Of course a PRNG generates the same sequence every time with the same seed, but that's true of every RNG, even a TRNG where the "seed" is your current space and time coordinates. To get more results from the distribution you have to use more seeds. You can't just run an RNG once, get some value, and then declare the RNG is biased towards the value you got. That's not a useful definition of bias.