What does this rod inside the my american classic seat post do?
I had a Peugeot bike once where the seatpost didn't have the usual clamp but a similar system to hold it in the seat-tube. The system was not very practical because if you wanted to adjust the saddle height you could only do so if the saddle was removed. The bolt was tightened from the top of the seatpost. There was a second draw-back: the seat-tube being rather thin walled you had to be be careful when tightening or you could ruin the tube.
Your bicycle has a normal clamp so I would remove this long bolt with the cone and save hassle and weight.