Dear Tammy,
I totally agree with what you are saying. This is especially powerful for us, lay people who do very little Dharma that our last act is to leave our bodies so it can benefit or save someone's life. However, I don't really think people these days are still holding on to tradition the way you explained or that they are even concerned about the pain. I think people are just too distracted with the pleasures and concerns of this life to really think about death. Signing up to be an organ donor is really facing up to the fact that we may die any time and there's a level renunciation in facing this fact.
However, if you from a Buddhist tradition like Tibet, there's a certain cultural norms that does not exists in other cultures. In Buddhism, death is not the end but a means from which we take our next rebirth as propelled by the winds of karma. Hence, in order to secure a positive rebirth, Tibetans use their body as a last offering of sorts. Tibetans practice sky burial and below is an explanation from Wikipedia...
Sky burial, or ritual dissection, is a funerary practice in Tibet, wherein a human corpse is incised in certain locations and placed on a mountaintop, exposing it to the elements (mahabhuta) and animals – especially to predatory birds. The locations of preparation and sky burial are understood in the Vajrayana traditions as charnel grounds. In Tibet the practice is known as jhator (Wylie: bya gtor), which means "giving alms to the birds."
The majority of Tibetans adhere to Buddhism, which teaches rebirth. There is no need to preserve the body, as it is now an empty vessel. Birds may eat it, or nature may let it decompose. So the function of the sky burial is simply to dispose of the remains. In much of Tibet, the ground is too hard and rocky to dig a grave, and, due to the scarcity of fuel and timber, sky burials are often more practical than cremation. High lamas and some other dignitaries may receive burials so as to honor them in death, but sky burials were standard practice for commoners.