Canal Road is owned by and maintained by DC. The C&O Canal is NPS. I think DC owns the stone wall that keeps the road from becoming one with the canal.
I commuted home frequently along Canal Road from mid-80's to mid-90's; it indeed never had the overhead X's and arrows, but in addition to neon Do Not Enter signs at the intersection with Foxhall Rd, it did have electric signs along the right shoulder that (when not obstructed by branches) would let you know how many lanes you should be using (either 1 or 2; there was no 0) with red neon tubes. The short stretch between Arizona Ave and Chain Bridge is 3 lanes (that would change at different points depending on morning/evening or regular), and that stretch had about as many "# of lanes signs" as the main stretch. There were also several signs facing each direction at the Arizona Ave intersection (more red neon). Long before those signs were removed, the numbers stopped lighting up properly. It was also said that the road's location in a valley wouldn't let the radio signal get through to change all the signs reliably.
Only once did I come around a bend in the left lane and find a car facing me. They'd already stopped and were pulled pretty far to the side. At that stretch, I can testify that the road is wide enough for 3 vehicles...
On Connecticut Ave one evening, a friend of mine was driving in the "rushhour left lane" and hit a vehicle that was turning left from the "normal left lane". Fortunately hit the front part of the driver's door at an angle, and nobody was seriously injured.
NPS owned reversible roads are generally controlled by motorcycle police and aesthetically-pleasing white sawhorses, which when not used to block traffic are of course left at the side of the road to add to the scenic quality of the area.