It would be better to update browsers, to display a different warning, in a place where a page can't change at all. (And while we are there, Firefox, please, do the same with the master password dialog.)
But I doubt any of them will do that because, security be damed, it messes with the minimalist fashion.
It would still be helpful even if they just modified the warnings to bleed into the non-page portion of the window somehow. It doesn't have to compromise minimalism. They just need to be creative about it.
But I think the best place for it would be between the tab bar and the location bar.
But I doubt any of them will do that because, security be damed, it messes with the minimalist fashion.