Why don't all GA aircraft have yaw dampers?
A yaw damper means added cost, weight, complexity, and one more system that has to be maintained. That's the downside. The upside, for most GA aircraft is that they relieve the pilot of having to make a "coordinated" turn. In other words, having to apply appropriate rudder input along with aileron input. Is that convenience worth the downside when the pilot has internalized doing that without having to think about it? That's a matter of opinion. For myself, a yaw damper in any of the, say, single engine Cessnas would be a waste.

There are some GA aircraft that could benefit from a yaw damper in other than banking into a turn or leveling from a turn. For example, in level flight the old V-tail Bonanza would yaw around the vertical axis in turbulence to an objectionable degree in my opinion. Very uncomfortable, especially to passengers in the back seat. It would have been great to have had a yaw damper.