Why ships of the line were rare on the American west coast

Why were frigates and ships of the line rare on the west coast of the Americas?

The voyage was long and expensive, while local threats rarely justified sending a battle-fleet unit instead of a frigate or smaller ship.

A ship of the line would have needed to sail around South America or cross the Pacific merely to reach the station. With no comparable local battle fleet to fight, frigates and smaller vessels could perform the required duties more economically. A Royal Navy deployment during the War of 1812 illustrates a region where a visiting warship could be the largest ship for thousands of miles.