Massive damage can put a player in death risk, but it won't necessarily won a battle, because his allies usually kill it before the downed character has made the three Death Saves.
And low-initiative monsters are usually cannon fodder. Because of the economy of rounds and battles, not many single piñata monsters, like let's say an ogre, can pose a threat to a party, because of the amount of damage that a single player can output.I'm being mastering D&D 5º since it came out, and I have directed two different tables, and I find ot several things: