Maybe its a matter of personal taste, but Vue as a standalone SPA (with a phoenix JSON API) is way easier to work with than trying to integrate directly into phoenix. Not to mention the logical separation of concerns (e.g. you can’t just assign everything on a conn and hope for the best).

Edit:
Rereading the question again, why use Vue at all if you want to do purely SSR?

Does Vue contain a server? I thought it’s a frontend framework. In any case you should use Phoenix to serve the HTML and the related JS/CSS files. There’s no reason to have two servers on the backend where one can do the job.

I have developed with both a. Phoenix at front-end and b. VueJS on front-end with Phoenix on back-end including authentication and authorization.

My suggestion based on my experience is to use Phoenix on front end while integrating some VueJS components as needed in the html.eex files (if VueJS is used to render data from the server, then JSON based API end must be used, i.e. render results as JSON to be consumed by VueJS).