While you are correct that flights are restricted, they do make changes according to weather. Prevailing wind changes will result in either a northern approach or a southern approach. The approach from the south essentially results in no view of the city at all except on landing. The approach from the north can result in a spectacular view of the city from the left-hand side of the plane.

Also, when the cloud ceiling is very low the northern approach can shift as well, from a "follow the Potomac" approach to a more straight line approach. I am currently living under the north approach and the difference is quite noticeable from the ground. I don't know how noticeable it is from the air.