What problem does this feature solve?

I don't see a good reason not using html native [hidden] instead of v-show directive. Even hidden used as a prop of component, it should behave like native one.

Related rule proposal on eslint-plugin-vue https://github.com/vuejs/eslint-plugin-vue/issues/1518

What does the proposed API look like?

N/A

It wouldn't work with transitions (https://github.com/vuejs/vue-next/blob/master/packages/runtime-dom/src/directives/vShow.ts)

A new directive could do but it should go through an RFC in the rfcs repository. Can you follow that if it still makes sense?