I think a reasonable compromise would be to have wallets refuse to use new keys without explicit authorization. If you backup the wallet.dat file, you are safe unless you hit "Yes" on the dialog box confirming that you have backed up.
might hit ok, remembering a backup 2 times previously, so it isn't fully secure.
+1000
Users may get bored by these alerts but that's perfect because it will encourage them to backup the wallet.
IMHO, the alert should disappear if the user has explicitly done the backup from the wallet (menu, ...).
If you just ask the user to confirm that backup has been done, it's likely that people will answer yes, just because they want to get rid of the alert.
An option might allow most advanced users to get rid of the alert with a simple confirmation but that shouldn't be the default behavior.