Being immortal really isn't that big of an advantage, unless the unit is defending your capital (in which case, you've probably already lost)
Since immortal units are teleported to your capital when they die, they're usually very far away from the frontline, especially given the general size of empires when divine essence comes around. Immortality preserves the unit's promotions, and saves you building a new one. But it still has to trek halfway across the continent to get back to the battle, which will generally be over by the time it arrives.
One way or another, killing an immortal unit takes it out of the battle. And stops it troubling you for at least a while.