I guess I'll post my reply in here since my own was marked as a dupe!
Anyway, strong disagree with gene.sis, coming from the position of someone who develops web sites.
Showing those dialogs is a web standard and an
expected part of browser UX. Since this behavior is expected, people will only find out that they need an extension to provide the functionality
after losing a draft. "People" includes myself, and those who responded to my thread, and the poster of this thread, and the poster of that
other duped thread, and the people who responded there. That's a lot of lost work!
Plus, to the concern of "needing to exit quickly," there are shortcuts on all platforms to advance the prompt and close the tab. It's typically just Ctrl/Cmd-W, Enter, as the close button is the focused element on the prompt for all major browsers and OS's. Those concerned with closing ASAP can simply press those two key sequences in quick succession.
Choosing to remove 1 step from a 2-step process and thereby allowing people to lose in-progress work is casting the baby out with the bathwater in a big way IMO. Heck, if we're
absolutely concerned with having a single hotkey escape hatch for users we can add that as an checkbox to the preferences, but it should be opt-in.
Auto-saving would be a great upgrade as well, but that doesn't replace a prompt! If the user closes in between the auto saving periods, this prompt should still be shown.
Plus, a prompt on exit is also much more easily implemented than any kind of auto-save feature (which still hasn't landed 3 years on from this thread!). You're typically looking at ~3-5 lines of Javascript using the beforeunload event:
https://developer.mozilla.org/en-US/docs/Web/API/Window/beforeunload_event