If you're logging in from a library computer, you don't want the hassle of putting your privkey file on it and wiping it later. (Or connecting a USB drive, which may be a security hazard for the library)
If you lose your computer, you still remember your password, but your only copy of your privkey may be lost. Losing hard drives is common for non-power users, because they don't do regular backups, and they often don't know that you can trivially recover files from, e.g. a laptop with a broken screen that won't boot.
And computerized cell phones are actively trying to convince those non-power users that files don't even exist, to protect their profits.
