There are also good reasons to keep your cosmology and monsters ripped off from a single source, from unity of setting to avoiding clashes.
They reinforce each other.
A world in which all myths are true is one in which massive contradictions are true. Keeping them more or less off-stage means there is no burning need to make them compatible. Even in so simple a matter as establishing that they fight, or have terrioritories, which are not the original myths. Saying that the nymph Echo is limited to the Greek regions, while the mocking dwarves that repeat your world are limited to the Germanic ones, is a small thing, but it's still not the myth. Are there many Wild Hunts? Or do the legendary leaders duke it out, and then the winner decrees whether they shall travel by land or air? Or are they all manifestation of the same being? A respectable pedigree there, but raising other questions, such as why one gets manifested here and one there, and what can you do to manipulate which one you draw?
If the conflict in a story is on scale with the Powers in it -- and if not, they're prone to be distractions -- there is the little question of power and winning. Could Olympus take on the Wild Hunt? What about the Things From the Dungeon Dimensions? And people being people, they will ask things like whether the Things are in fact the left-over Chaos, and whether they can be converted to more Cosmos.
And everybody's bound to be interested in it. If the forces of summer and winter are duking it out, all sorts of gods and powers will be interested in its coming out properly, even if they differ on what's proper. The only thing keeping it from being a free-for-all would be a higher power. And if there's one thing that these all-myths-are-true settings are weak on, it's higher powers. It is not invariably true, but most writers who write them seem unable to conceive of, or create convincingly, a power that is not a human being, swollen large, and oftentimes a three-year-old, swollen really large. A being that could not control except by raw power, which has exploitable weaknesses, and might easily lose that power to another. . . .
Given the difficulty of coming up with satisfactory answers to this, it's a good thing to finesse it.