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In the short term (single digit generations) that’s probably true, but I don’t see how it could be on longer scales. If the random mutations decrease fitness, they won’t be passed on at some point, since there is less reproduction. If they increase fitness, they will be passed on to more individuals.
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What OP said is Motoo Kimura’s Neutral Theory of evolution. There’s a lot of evidence supporting it. The vast majority of mutations have a negligible effect on fitness. So it is very possible that something may evolve purely by chance.