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Monte Carlo simulation doesn't generate all classical probability distributions though. Attempting to do that would be nuts. Monte Carlo simulation only samples from a single, fixed distribution (or maybe a small number of distribution).

I'm not super convinced by the argument based on number of parameters either, but your analogy doesn't refute it at all.

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Its not meant to be an analogy.

We also will not attempt to generate all quantum states on a quantum computer. As with classical monte carlo, we will only ever generate a tiny fraction of the possible quantum states/distributions, and will also sample from a fixed distribution (whatever the quantum circuit outputs, we measure it in a fixed basis and always draw samples from that single, fixed distribution).

We will also achieve robustness against the tyranny of the real numbers in our gate parameters in a very similar way that a classical computer does when it approximates some idealized Monte Carlo algorithm.

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