Protecting the airspace / groundspace of the capital seems like a reasonable training mission. Flying over the Potomac means any crash doesn't hit residential areas, unless they are unlucky enough to hit a bridge.
Sure but you can train around DC without crossing the final approach of the commercial airport that has 380 flights a day.
I think the Potomac flight paths were a post 9/11 thing. They were confined even further in 2020. But what that actually means is that the commercial jets are only and always in very specific airspace.