How about making it 'harder' for the user to close the browser when there is an alert being shown by a website ? For instance, if google docs throws an alert about the data not being saved, your browser could throw you a msgbox notifying you that such tab has an alert you haven't dealt with when you try to close it.

Yes, that's a lot of msgboxes, but it's a decent compromise I think. It's not like that would happen very often anyway.

Google docs and Gmail and many other top 100 sites use on window unload. It wouldn't fly.