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But aren't there quite a few ways to design a well functioning eye? Compare insect eyes to human eyes to mantis shrimp eyes, and there are some pretty big differences.

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A given environment will give a certain kind of pressure and demand a certain kind of solution. Bring the ancestors of mantis shrimps to the treetops and neothlithic apes to the ocean floors and they would both die... If you fix that and let them somehow compete on vision they would likely converge on eyes like the those currently living in the environment have.

Don't insects and monkeys live in overlapping environments with radically different eye structures?

Path dependency. Insect eyes and vertebrate eyes presumably each occupy their own unique minima in the energy landscape. Even if we could describe a cost function that picked one of them as more globally optimal, moving from one to another would be hideously expensive.

It's also possible that compound eyes have an advantage at smaller eye sizes---or maybe a better way to put it: their disadvantage relative to vertebrate eyes is less pronounced for equally small eyes. Pure speculation on my part though.

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