I actually think there should be a FrontPress, instead of a BackPress.

Here's an example of such a project:
https://github.com/jgrossi/corcel

What I mean by that is all WordPress files do not need to be loaded on the frontend to display some data, like they currently are.

Things like the WP REST API would make perfect sense for this. Currently, the WP REST API is built out as a WP plugin, so you will require all the bloat that comes with loading WordPress in order to receive and respond to API requests.