GPS can be used to adjust the tiller on a sailboat short term. As long as it's moving about 1 knot or more. The compass heading is constantly changing with each swell, where GPS does not as much. With the appropriate feedback constants and timing you can steer up and down with each swell just like a human navigator would. When the speed is less than 1 knot, this is the best solution. When the seas are more flat, and speed >1 knot, only GPS is needed. I have been sailing and designing my own autopilots for 20 years. Sometimes out in the middle of the Pacific!
When you're cruising for weeks at a time with limited battery power you would not want to use the autopilot to steer up and down each swell. Mechanical wear becomes an issue. With light winds and smooth seas it is difficult to see a consistent heading with GPS, because of the slow speed. You are correct. But then you wouldn't need an update every 1 second. You can write your own code to calculate the heading every 10 seconds instead. There are only a few conditions where GPS alone without a compass is not appropriate, rough sea state with little wind. A compass is needed. But there are also many conditions where an electronic auto pilot fails to work efficiently, regardless of the sensor. During a storm I'd prefer a Windvane.
The absolute error can be 10m. But from one second to the next the error changes by only inches. So even when you're moving slowly, the line is straight when you plot it. Data can be obtained 10x per second with a modern GPS.