In several episodes of Futurama, Zapp Brannigan reminisces about winning one of his many "victories" using this tactic with human troops. What happened was there was an attack by "Killbots", in which he just sent waves and waves of his own men against them until they filled their pre-set "kill limit" and stopped.
There's also the episode where he plans to send wave after wave of ships to clog the enemy's weapons with ship wreckage:
Zapp: The alien mothership is in orbit here. * points to map* If we can hit that bullseye, the rest of the dominoes will fall like a house of cards. Checkmate! Kif:(sighs) Zapp: Now, like all great plans, my strategy is so simple an idiot could've devised it. On my command, all ships will line up and fly directly into the alien death cannons, clogging them with wreckage.
In that battle, under those orders, he loses half his fleet when they mistakenly attack the Hubble Space Telescope instead of the real enemy.
A Zerg Rush gives the Monarch's henchmen a rare and costly victory over Brock Samson. It was possible because they were in the middle of partying and getting tattoos which... increased their morale enough to just dog pile him while he was distracted.
They later use the same tactic to bring down Guild Wasps; fighter jets piloted by Guild of Calamitous Intent Elite Mooks. They just pile on to force the Wasps to crash, and, in at least one instance, suicide dive into the engines.
The aptly named "Rush" in Wakfu. The favorite pastime of the Shushus, those who invoke it are pitted against 666 low-level Shushus until they fall. When the heroes face it, they also have the added challenge of fighting Anathar.
This is the primary strategy of the Generator Rex villain No-Face, who telepathically directs all of the EVOs at strategic points to overwhelm opponents who are attempting to escape.
EVEN worse, an individual chi blocker was a competent and dangerous opponent even for main characters. They were skilled enough to actually win in one-v-one fights against the series main character. A highly coordinated rush on top of that was basically overkill for most enemies.
In the Hanna-BarberaRichie Rich, Irona faced a group of inferior impostors all charging at her at once and she simply converted her lower body into a large roller and flattened all her attackers at once.
The animated mini-movie of Hero Factory has this done with kaiju, of all things.
The Powerpuff Girls: In "Twisted Sister", the girls get rushed by a mob of prisoners that Bunny inadvertently set free, and they're powerless to do anything about it until Bunny swoops in to save the day.