There could be many interpretations if this is a fictional or fan - created story. Maybe 'kakyoin' is a character in a particular universe, like a game or a comic, and the idea of laying an egg is some sort of strange or magical event within that context. But without more information, it's hard to say for sure.
The concept of a'superior' Pokemon laying an egg in fanfiction could be related to a unique power - up or transformation. Maybe the act of laying the egg is not a normal reproductive process but a way for the Pokemon to transfer its power or knowledge. For example, the egg could contain the essence of the superior Pokemon's abilities and when it hatches, it gives rise to a new entity with combined powers. This would add an interesting twist to the Pokemon fanfiction story.
Others could be excited. They might see it as an opportunity for a new and powerful Pokemon to join their team or be part of their world. They would likely start making plans to protect the egg and ensure its safe hatching, perhaps even researching about it to find out what kind of Pokemon it might become.
Another fictional hawk could be 'Hawkeye' which is a name that can be associated with a hawk - like character. It gives the impression of a character with sharp vision and a focused, predatory nature, much like a real hawk.
The Hawks' back story could involve their origin as a sports team. They might have started in a particular city with a group of passionate players and investors. Maybe they were initially part of a smaller league and then grew to be in a major one. Their name could be inspired by the characteristics associated with hawks, like speed and precision.