It’s a fair question.  A receptacle would surely make it convenient for people to drop their trash in as they leave the property. Unfortunately solving this problem would create a list of other, bigger problems:
Since Newark Street is not a bus route, there is no DC garbage pickup. As an all volunteer organization we don't have the man-power to empty cans regularly. The trash cans (at best) would be filled with dozens of poo bags and be especially foul in the summer. Public trash cans also invite drive-by dumping of garbage. Because the local animal population will undoubtedly “volunteer” to pick through the trash and scatter it around the park, we think the scene could get pretty grim, pretty fast, and that's not fair to our neighbors.
The sad truth is that trashcans have substantial downside as demonstrated in the various photos shown below which were all taken within walking distance of Rosedale. These trashcans are eyesores to park users and neighbors. They are used to dump all kinds of things including clothes, furniture and large plastic bags of unknown content. They require a permanent structure which is contrary to Rosedale’s charter of historic preservation. They require foot traffic to and from a fixed location which results in bald ground and erosion. Often there is trash on the ground around these trashcans which results in vermin. They are also targets for graffiti. Cans either use plastic liners (resulting a waste/poop “soup" when it rains) or not use liners which results in more trash on the ground. Whatever marginal convenience is outweighed by these realities.
So, while it takes a bit more effort, like the National Park Service, we continue to ask that you “pack it out” and “leave no trace.”