Adding a mode makes the interaction with it both modal and more complex.

Compatibility modes are confusing and user hostile, and two different methods of interaction increasing testing requirements.

Increasing testing requirements on what? I meant adding it to the browser (or the window manager/X/whatever), which would not require a massive effort to test. The websites themselves already have to support (at least) three modes of interaction if they want to have all main browsers supported (mouse, touch, keyboard).