They typically don’t have hotels in range of the train station, and since Amtrak is once a day service an overnight stay will happen. Stations are often in the run down part of town, so while you can walk and find things, there isn’t much (it looks unsafe, but I generally think it is safe)

Also many of those “lesser” cities are tiny - sure you can walk the downtown, but there isn’t much there. In my travels on Amtrak my impression is the majority of people are not going for the downtown - there are plenty of stores closer to home. You are going to visit family, or some attraction not close to the station.