Wait, this is news to me - which VPS providers do not have persistent data storage? Are you thinking of Heroku-like deployments? I feel like every VPS provider I've encountered always listed storage as a feature?
Just to point out, if the data is important you'll want backups anyway. Even with S3.
Just in case. :D
Much more likely, though, is that you, or some sysadmin at your company, or even some user will accidentally hit the "delete" button on something important, and then without a backup, you can't get it back. Which is honestly the thing that people usually need their backups for, anyway. This is what most "data loss incidents" are: people just messing up and deleting things they shouldn't have. Wetware is much more prone to failure than hardware, after all.
In case something goes wrong. ie your account has a problem unexpectedly, or if they do indeed have a data loss/corruption problem, etc.