No, not only do you have to leave from the airport in Changsha, but you can’t even leave the jurisdiction of Changsha!
Not even “stopovers” are allowed. For example, if your air itinerary is like this: Rome -> Changsha (72-hour stop) -> Xi’an (a half-hour stop without even getting off the plane) -> Hong Kong, then you can’t request an exemption because your itinerary includes two Chinese cities.
Obviously, there are exceptions in provinces where you can travel freely for 72 or 144 hours. For example, if your flight arrives in Shanghai, connects in Hangzhou (which is located within the same 144-hour region of Shanghai, which is the important thing), and you then leave China before the 144 hours expire, there’s no problem.