I sometimes drive a F250, crew cab, short-bed pickup. It’s a TANK, parks like crap, and I found a Prius stuck in the wheel well. I avoid my narrow old town streets and can’t imagine having to drive it in DC.
A “if your vehicle can’t park inside the box” rule, and a “vehicle cannot extend into the driving lanes when parked or the parking areas when driving” rule for narrow streets would keep the behemoth vehicles out of the congested areas.