Mob spawners such as zombie spawners spawn monsters way too fast (often 6 at a time) to the point that it is nearly impossible to kill them all before another set of 6 or so spawn even with a diamond sword on creative mode.

To reproduce: Create a world in creative mode and peaceful difficulty using seed 493056156 . Then teleport to coordinates 28, 46, 129, find the spawner nearby, and set the difficulty to easy mode. You will see that around 6 zombies spawn at once and any killed will respawn almost instantly.