This feature was on a forum that I used before (MyBB) and I used it all the time.
Basically there was a directory in the admin folder named /backups/

When making an SQL backup, you had the option to create the backup in that directory, instead of downloading it.
Maybe a similar feature could be included in IPB?

Just a suggestion :)

Doesn't sound like a bad idea +1

Yes, backup/restore from within IPB would be quite nice.