If it has already integrated git, why not support syncing through the VCS instead of third party like Dropbox or iCloud? Is there any note taking app that automatically syncs changes with a remote repository, so I can simply provide credentials to a hosted git instance and it does everything out of the box?

There's a Git plugin for Obsidian: https://github.com/denolehov/obsidian-git

It's not quite out of the box, but installing community plugins is very easy through the settings UI.