You can install any SQL variant yourself on any web server. I can be on the SAME MACHINE. Even a vps! Boom!
Everyone used to do it all the time. For some reason everyone decided to pay more for less power and use the cloud instead.
You still won't go above 20% CPU for even moderately complex CRUD applications.
If you're really crazy you can add a cron job to send a backup each night to S3.
And it'll take you all of an hour to do that.