Seems like there should still be enough context. A user risks lost workflow if they've done nontrivial form entry. Exactly where you set that bar may be debatable or measurable, but certainly there is a difference between a partial search query and a full address form, for example.
Alternatively, the browser could just play it safe. I recall at one point the old Opera would prompt if unsaved form edits were present, on any navigation attempts (clicking away or browser back button/backspace). This saved me on many occasions and I never remember being annoyed by over-notification.
> You said yourself, they released an extension for this.
Oh was there an official one? At the time, the only extension I could find was some slightly-sketchy third party one that allowed you to set hot keys for many things.
> This requires too much page context. A search field being partially filled is very different than a long registration form being worked on.
I don't know when they did this, but Chrome also seems to remember form input when you back out, and re-fills the form if your reverse the backing out. That's a better solution than changing the shortcut because it works if you back out by other means, too, such as clicking the back button with the mouse or using the back gesture on a Magic Mouse.
Firefox does it to.
This has saved me many a time when I've accidentally done a back gesture on my Magic Mouse while composing an HN comment.
Sometimes, unless the flow is made of multiple pages of forms. Press back, you get to the previous form (with the fields now empty obviously), press forward, get a server 500 error.
In a nutshell, it feels like browser makers do their best to improve user experiences, and website designer do their best to ruin it again.