Good question and this was a debate during the feature design. In the end, the goal was to not conflict with Obsidian’s native theme handling functionality.
So BRAT provides a shortcut to adding a theme to Obsidian’s theme manager but then leaves it up to Obsidian to handle updates the way it does.
BRAT is mostly for testing unreleased plugins or themes. So it has to do its own handling of version control and downloading support files. So if a user wants to use BRAT on a plugin or theme shipped to the community they can, but BRAT treats them as if they are in beta testing.
Its a subtle distinction, but it allows BRAT to do its own thing, also provide some conveniences to the Obsidian feature set, but not step on each other’s tools.
I also have the dilemma I don’t want to work too much around Obsidian’s plugin and theme installation features because of security and safety. With BRAT, you are taking the responsibility to know what you are installing, from who and why. When something is in the community lists, its assumed some due diligence has been done on those downloadable features.
So it can be done, but it isn’t done due to keeping some boundaries between BRAT (user based responsibility for installs) and Obsidian (vendor and community based monitoring) for installs.