This is common on long distance trains running on the Northeast Corridor, including the Cardinal and Crescent. They only drop off passengers northbound and pick up southbound. Since the NEC has service much more frequent than on most long-distance trains, so generally someone travelling on the corridor only can usually find a train to take without using a long-distance train.
The reasons mentioned above are valid. In addition, it means that there is more room for the long-distance passengers. By not allowing passengers to board from WAS to NYP, the space is available for someone travelling from, say, Miami to NYP, who will pay more for their ticket.