Why are isotopes that have relatively short half lives the only ones used in medical diagnostic tests?

Radioactivity is generally bad for the cells of the body, because they may get ionised by it, which means that damage will get caused to them so that they may die. Hence, it is less preferrable to choose an isotope to enter your body, which will emit radioactivity for a long time, so we tend to choose isotopes, the radioactivity of which ceases quickly, so that the least possible amount of damage is caused to the cells.