Code splitting a single page app is a great way to improve its initial loading speed. Since a user doesn't have to download all the code in one hit, they'll be able to see and interact with the page sooner. This will improve UX, especially on mobile, and it's a win for SEO, as Google penalizes slow loading sites.
Last week I wrote about how to code split a Vue.js app with Webpack. Long story short, anything you wrap in a single file component can easily be code split, as Webpack can create a split point when it imports a module, and Vue is happy to load a component asynchronously.