This isn't even a design mistake or in-game joke, but actual Japanese folklore.
Here is a comparison picture of a common Tanuki statue in Japan:
The Japanese raccoon dog (Tanuki), just like foxes (Kitsune) is widely believed to be a shapeshifter and prankster with human intelligence and certain magical abilities, one of which is that he can enlage his testicles to stretch over eight tatami mats (approx. 12.4 m² / 133.4 ft². ). There are classical depictions of shapeshifted Tanuki basically teabagging humans to death, using their own dangly parts as drums or carrying them over their shoulders like backpacks.
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But where did that unusual ability originate from? It's not like some Japanese scholar woke up one day and went "Y'know what folklore needs? Huge friggin furry BALLS!" or something like that.
The origins of the Tanuki testicles are rather mundane:
That myth is thought to have developed during the Kamakura era, where goldsmiths used to wrap chunks of gold in tanuki testicle hide to pound them into the thinnest of gold leaf. Tanuki leather is extremely tough yet flexible, so it was said to be able to stretch the gold into a sheet large enough to cover eight tatami mats without the leather breaking. Wallets made of tanuki hide became popular (often made out of that leather because it was conveniently bag-shaped anyway), as it was believed they could stretch other kinds of money as effectively as they stretched gold, and the depiction of the tanuki’s bodacious ballsacks stretched along with the legend.
Since the creators of Ōkami thoroughly researched the IRL lore they wanted to use for the game, it is no surprise that the Tanuki statues in the game also look as well-endowed as their real world counterparts.
