Do all A bodies have overheating problems?

Your fan is the problem. It's that simple. If it cools cruising down the highway, the radiator is good. My "problem solver" is a factory flex fan. That usually cools anything at idle. I don't run shrouds either. If you don't like the flex fan, try an electric or clutch fan. I've run A Bodies as daily drivers for 40 years. They do not run hot. None but a very few were stock.