Strong evidence that a search algorithm can find high functionality in an astronomically large search space

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You keep appearing to assume that functional proteins are randomly distributed in search space.

This is not the case - for example, average globular protein consists of ~31% alpha helices and ~28% beta sheets.

https://www.letstalkacademy.com/publication/read/protein-structure-protein-secondary-structure-protein-beta-sheet

If virtually all functional proteins have alpha helices and beta sheets, can you then see why another functional protein may be a short distance in sequence space from another?