Hasn't this been extensively discussed already?
The topic of Vue+Drupal has been discussed, but they had to do with choosing a framework for the Decoupled Admin UI component of Drupal's Admin UI & JavaScript Modernisation initiative.
This discussion is regarding the addition of Vue to improve existing core JavaScript, not to create an entirely new decoupled admin UI.
(It's also worth noting that progress on the Decoupled Admin UI stopped ~2 years ago (as of Spring 2021) and it is unlikely to resume)
For reference, those prior not-directly-relevant discussions can be found here #2913628: Proposal to use Vue.js for building Drupal’s administrative UIs, and here: #2913321: Proposal to experiment with React for building Drupal’s administrative UIs.
Problem/Motivation
I explored Vue as a possible replacement for Backbone, a seemingly inactive library that needs to be removed from Core. #3145958: Re-evaluate use of Backbone.js in core. I built prototypes for replacing Contextual's use of Backbone in Vanilla JS and Vue. The Vue prototype was easy and pleasant to build! It did an excellent job cooperating with preexisting JavaScript, something I'd never experienced with a declarative framework. Vue seemed like an option that could be gracefully added to Drupal without requiring the massive changes of the now-dormant Decoupled Admin UI.
However, the Vanilla version of the Backbone replacement did its job well enough that I couldn't justify the addition of Vue based solely on it replacing Backbone. The Vanilla version is less concise, but it absolutely gets the job done without all the concerns that come with adding a large library.
What should be happening in THIS issue?
This is to get feedback regarding the ways that the community feels adding Vue could benefit core. For example, I discovered that Vue is a great replacement for Backbone - great benefit, but not great enough to justify core inclusion.
There seems to be sufficient information regarding why Vue itself is good, so it's probably best to focus on the specific problems/features that would be improved by having Vue around.
Full disclosure: this issue summary was written by someone enthusiastic about Vue. It's also an acknowledgement that there needs to be concrete justification for why it should be included. This issue could just as easily demonstrate that there is not enough incentive to add it as a library