If you take off northbound, you only have a few seconds to turn left with the river before you’re over DC and into restricted airspace. If you take off and obliviously fly straight, it’s too late. It’s not a wide river.
Once you’re across the river, turning left is way worse (takes you directly over the federal complex), so ATC told them to turn right to exit the restricted airspace. That would take them around over SE DC.
Yeah. No joke. it is even on the departure chart: "Departing Rwy 1 requires expeditious intercept of outbound course to ensure avoidance of P-56 boundary"
Taking off north-bound (runway 1) wouldn't give you the option of flying up the Anacostia (the right spur that bisects DC when looking at a standard map).
Taking of north-east (runway 4) would give you the option of taking the Potomac (left) or Anacostia (right).
I've never seen runway 4 used. It's usually a north flow using 1.
Once you’re across the river, turning left is way worse (takes you directly over the federal complex), so ATC told them to turn right to exit the restricted airspace. That would take them around over SE DC.