> My one complaint is that Vue components place templating, code and styles in a single file and I'd prefer a directory with three (or more) separate files.

You can have that. You do need an index.vue file containing something like:

    <template src="my-component.html" />
    <script src="my-component.js" />
    <style scoped lang="scss" src="my-component.scss" />

If you put that into a directory called my-component/ then you can just do:

    import MyComponent from 'my-component'

…and it will pull everything in.

I don’t think it’s a requirement. You can use Vue simply by including it from CDN and just sprinkle some functionality on a page.