Chazal despaired of death because it would interfere with their great joy in engaging in Torah and mitzvos. In the animal world, the specific animal is a representative existence of the class but lacks individuality. The human exists not only as a representative of mankind but also as an autonomous, unique existential experience. Death of the precious individual is absurd and existentially abominable.
Spiritual death frightens man most. Tumas mes is a result of a trauma born of the reality that death defeats everyone eventually. It is a form of impurity that represents man’s tragic and inescapable destiny. It would be incongruous to employ the same purification process for tumas sheretz for tumas mes. The latter requires an additional form of cleansing besides tevillah, the sprinkling of the third and seventh day.
Hashem, the ultimate cleanser, will free man from death and its associated defilement in the eschatological age. Until that time, we must battle death to the fullest extent possible. We must act as proactive object and practice tevillah, and do anything possible to extend life through an organized scientific effort. Judaism believes that longevity is a goal that can and should be achieved, but not immortality.
Death will plague man until Hashem removes that curse for all time. Man can redeem himself from the fright and defilement of death through tevillah, but ultimately he requires hazaya, trusting that Hashem will sprinkle purifying water and complete the cleansing process, eliminating death and its associated defilement forever.