>But paper is pretty effectively recycled and trees aren't the only input - transport, water, and heat at the plant.
Exactly.
Moreover 1ha of Arundo produces 20-50t or more dry mass per year packed in 100mx100m area. Granted, not harvested at 0% humidity, less dense than paper. Collecting 50t of recycled paper from the containers in the city probably needs more energy for transport.