It's a (single file), which would look something like (idk how to format code on h/n lol):
<template> <ul> <li v-for="message in messages">{{ message }}</li> </ul> </template>
<script> export default { data () { return { messages: ['hello', 'world'] } } } </script>
I realize this is a completely trivial example, but is this what you're getting at? Everything related to that component is in a single place. The template itself handles any UI specific logic: conditionally showing an element, looping, binding an event.
Any real logic is going to be handled from the component itself.
That said, Vue actually supports using a render function as opposed to using a template. You can even use JSX if you want (though I certainly wouldn't consider JSX a first class citizen in Vue).
This kind of system is extremely common on the backend---Python's Django and Ruby on Rails, to name a few frameworks follow the practice of templates being given data and simply acting upon it.
Since these are dynamically typed languages, there's no IDE typing support in the template.
There's just testing.
As someone who uses Django regularly, I can say there's a huge swatch of territory between "small examples" and "large projects".
That territory can easily cover teams of 19, and multimillion dollar projects.
That's my whole contention -- Vue is just a better iteration of the same old painful experience. React actually solves the problems I have.
If you aren't using a data store, your parent component would solely be responsible for mutating data. If the child component needed to alter it, it would raise an event that the parent would listen to and make whatever modifications necessary.
I'm having a lot of trouble truthfully understanding your "mental back-and-forth" issue and I'm wondering if it's an inexperience with Vue issue. Give it a try... I'm willing to bet you'll love it.