Does it make sense to write FSE theme-template edits to a child theme?

[johnstonphilip]

When editing an index.html, 404.tml, single.html, theme.json, or other theme-specific files with the Site Editor, the changes get written into the database.

It would seem to me that these are more naturally written to a child theme, since that is the purpose of child themes: to store user tweaks to a parent theme.

Obviously this would require "write" permissions, but so do many other WordPress functions like uploading media, installing plugins, and doing auto-updates.

Thoughts?