Autodesk need to add a built-in setting in the Revit Options menu under "File Locations", where you have an option to activate a "backup folder" option or not. This setting can have an option to create a backup folder in the same Revit Project/Family/Template location, or you can choose a specific folder location where all backups can be saved to. Personally, I would prefer all backups to be saved in a backup folder in the same file directory as the Revit file.
This helps also with server backup software which can be set to exclude specific folders (like backup folders) from being backed up and causing the backup drives to fill up quick with unnecessary clutter.
These are simple additions that Autodesk can make to the Revit software instead of getting other third-party apps.