No, you should not be making backup copies of your website’s data and storing them with your web host. The purpose of making backup copies of your site is store them on a different computer system. If your web host were to have all their hard drives blow up. You would have no access to backup copies of your website.
If you had stored all your backup copies with your web host and your web host lost all your data. You would have no backups. Your backp copies should be stored on either your local computer, another web host, on a online backup service, or a USB stick you carry with you. Your backup copies should never be stored on the same web host that you are making backup copies of data from. This defeats the purpose of having backup copies of your data.