The problem is that the onset of death is not so obvious. We really don’t know, scientifically, what constitutes physical death. Is it when breathing stops, when the heart stops, or when there is no brain activity? In spiritual terms death is when the soul leaves the body.
Priests are not able to discern exactly when this occurs. No physical event defines when the soul leaves. No "vacancy" sign pops up. Once all activity associated with life is gone and the process of decomposition begins, then it is clear the soul is no longer present, but at what moment the soul left we can’t tell. Unless he is sure death occurred, a priest should perform the anointing (Jas 5:14-15).