Nope, not going to happen. At least one good reason and that is that if Rackspace leak your data via a backup they're going down to the tune of millions.
Yes it would be nice if Rackspace could speculatively create a backup but they'd be dancing on ice doing so.
Here's something I don't get: didn't Rackspace have their own daily backups of the production server, e.g. in case their primary facility was annihilated by a meteor (or some more mundane reason, like hard drive corruption)?
Regardless, here's a thought experiment: suppose that Rackspace did keep daily backups of every MySQL instance in their care, even if you're not paying for the backup service. Now suppose they get a frantic call from a client who's not paying for backups, asking if they have any. How much of a ridiculous markup would Rackspace need to charge to give the client access this unpaid-for backup, in order to make the back-up-every-database policy profitable? I'm guessing this depends on 1) the frequency of frantic phone calls, 2) the average size of a database that they aren't being paid to back up, and 3) the importance and irreplacebility of the data that they're handling (and 4) the irresponsibility of their major clients).