It also does track the revolution of the Earth around the Sun, and that of the Sun around the Milky Way, as well as the various influences over the Milky Way that make it go less than straight on its way towards the Great Attractor.
Those movements just happen to be slow enough that they don't limit image stabilization to 6.3 stops.
The relevant "speed" is the change of the direction you are pointing at. The Earth rotates around itself in 24 hours, but around the Sun in 365 days, so the daily rotation is 365x as fast. We also rotate around the center of the Milky Way every couple of hundreds of millions of years.
At least with respect to the influence of the Earths rotation. With respect to compensating actual camera shake, the modern systems correct 5 axis's. 3 for rotation around the 3 space axis's, and 2 translational, which leaves only motion towards or away from the motive uncorrected for (which usually only expresses itself in the need of refocussing, but that usually is far beyond camera shake, except for macro photography).
Per my other comment: Earth isn't attached to the sun, the sun isn't attached to the galactic center (they are orbiting). They are independent rotational frames of reference. They are also gyroscopes in their own right.
As far as taking pictures of other things on Earth, at least. Taking a picture of another planet/star/galaxy would also face similar challenges.
What's the difference between our "attachment" to Earth compared to Earth's attachment to the Sun? Aren't both doing circular motion due to gravity (in us-Earth's case, gravity + support force from the ground) and inertia?
I never thought of that one. It's fun to think "we know the whole universe isn't spinning very fast, because our gyros are stable". Feels both obvious and somehow bigger-than-life to me.
We are not kinetically bound to the galactic center, there is no friction causing earth to remain "upright" in respect to the galaxy. Earth is also a freely rotating inertial body and, even though wobbly, it is itself a gyroscope.
The next level of stabilization would probably be gravitational waves.
Those movements just happen to be slow enough that they don't limit image stabilization to 6.3 stops.