Can I download Home Videos directly from Apple TV?

The syncing from computer to mobile was always supposed to be a one way direction. The originals were supposed to stay on a computer (and/​or other storage) as well. There is no official method to sync in the other direction.

Users are strongly advised to have backups of all their personal computer files. How to back up your Mac - Apple Support. There are only two kinds of people: those who have lost files and those who have yet to lose files for not backing up thoroughly.

There were once third party apps that claimed to be able to retrieve user content from iPhones. I think those did so by examining a local non-encrypted backup of a phone on a computer. Such a backup isn’t easily readable on a file level, though, hence the need for a specialized app. And I’m not sure if that method is still available for current versions iOS; it might not work that way anymore. None of that was endorsed by Apple, though.