Shibas are #1 in Japan for dog registration for both Japanese breeds and breeds in general. Because of their size and popularity in Japan, I can see why they on occasion appear in anime and memes.
However, what I don't get is why the #1 in fame for the Japanese breeds, the Akita Inu, may not as popular with memes. The breed would have gone extinct during WW2 had it not been for Hachiko likely being the main factor in their salvation. Keep in mind, the Akita Inu is the largest Japanese breed for the spitz-group. Keep in mind, the Akita Inu is the largest Japanese breed for the spitz-group.
The #1 in size for the Japanese breeds is the Tosa Inu. As mentioned by the "Tosaken: Kochi’s Mastiff" article on the Life in Kochi site: "Tosaken [I have read that while both "inu" and "ken" are Japanese for "dog", the former is for singular and the latter for plural] and Akitaken’s withers heights are similar. It is about 60 cm. Tosaken’s weight is bigger than Akitaken’s. Tosaken is about 90 kg. Akitaken is about 54 kg. Tosaken and Akitaken’s life are similar. It is about 10~12 years."