Depending on the fish, it is possible or usual. Afterall, if the bones are small and not bot bothersome to eat, why would you take a lot of time for bone extraction? That is the general motto for classic types of cooked fish such as shown in this manga.
@SirBatu
Yeah, well after I wrote that I remembered sardines and anchovies are a thing- thanks to Stardew Valley. You also made an excellent point, so had I not I'm sure you'd've convinced me!