Akeeba Backup creates a site backup that can be restored on almost any hosting. It creates a full backup of your site in a single archive. The archive contains all the files, a database snapshot and an installer similar in function to the standard Joomla! installer.
Manually downloading all the files is not an effective use of time or disk space. Typically, sites have around 4000 files and that would require a massive amount of space on a compluter or cloud storage platform.