Players don't worry about enemies standing back up. They hit zero hit points and they're dead forever. PCs, on the other hand, can easily be revived to full fighting capacity within seconds. Fifth edition goes way out it's way to ensure its heroes don't die. The rules support "not dying" in about every way imaginable, and I don't personally like it as DM because without the threat of death there's no drama. Sure, it can be houseruled away (and I do to some extent) but they still don't like attacking a downed foe. I think it is necessary to do so in the context of the rules the game has established to ensure tension.