[puzzledobserver]

Is it? Think of a single star during a galactic collision. It wants to collide with every star in the other galaxy. It gets pulled this way and that, so, in sum, it decides to collide with the oncoming galaxy as a whole. Unfortunately, despite having billions or trillions of stars, that other galaxy is mostly empty space. The poor original star that we were tracking was unable to collide with any star at all.

[thaumasiotes]

Well, why do we keep attempting to collide with the Sun instead of striking out for the center of the Milky Way? Everything you just wrote applies just as much to the Earth as it does to a star heading through a foreign galaxy.