Yes - self steering works on boats with longish keels that track well and are well balanced. In my experience well balanced means depowering the boat. My boat, a Nordic 44 has a low aspect fin keel and does not track well in downwind/tradewind conditions. Big waves hitting the boat on the stern quarter push the boat off course and the windvane is not powerful enough to get it back on course. The friction of wheel steering robs the windvane of a lot of it's power. I have tried.

Electric autopilots don't care about weather helm. They steer to a magnetic or wind direction course with far more accuracy than a windvane. Yes. they cost more but IMO they get you where you want to go faster and more accurately.

When you figure in the cost of making electricity from solar/wind/water the cost is even worse than your "twice as expensive" but looking at cruising boats today the trend is clearly away from windvanes.