You can just as easily apply the same tabindex to a div though.
> Only if document order is sane. Usually with modern websites it isn't...
Well that's the real problem, all your non-interactive content (like text) is going to be out of order too. You're just adding to the confusion if buttons and other inputs are in a different order from the content they're associated with.
> Otherwise, he will pointlessly tab through search, menus, cookie bars and a ton of other pointless stuff first.
The proper way of dealing with this is a "Skip to Main Content" element: