Yeah, I cannot imagine being able to see much further than 300km
anywhere in the world. Even from top of the Alps I doubt one could see even as far, considering that the flat ground around the Alps will curve behind the horizon very quickly.
The trick is to be quite high up oneself and then be looking at something massive that is far away. Let's remember that Mount Rainier massive (4,392 meters!) and even then it is almost completely hidden by the horizon!