Firefox and Chrome give me that warning page, but I just click on "Advanced" and it will let me continue to the website. At least for me, it's just a huge warning to be careful but I still have ultimate control.
The "owner" is no longer in control, and has not been ever since the web became "app-ified".
Browsers could have bright red flashing lights telling users that they're currently being phished and users would still enter their credentials because doing nothing isn't seen as a meaningful alternative action.