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Dark Beasts have always been a thorn to Humans and Migas alike
Eulogeo wasn't included because Dark Beasts are rarely left to grow
Each Eulogeon is a powerhouse capable of taking groups or even armies depending on their strength so they easily wiped out Dark Beasts.
Instead, they had problems with the Dark Beasts that somehow survive and grow.
Those tend to be at least 3 to 5 times stronger and durable than the standard.
The explanation for this is because of Eulogeo's prosperity of ether.
The more focused the amount of energy in the world is, The more the occupants of that world benefit from it. Dark Beasts were not an exception to that rule
Humans have often had the most problems with Dark Beasts being the weakest amongst the 3 races.
Migas had fewer problems due to being stronger on average.
Irrespective of the ease of handling Dark Beasts among the races, none of them would want a stampede to occur.
Because wherever the stampede went.