Perhaps Goku would form a different kind of bond with his friends. Instead of a marital relationship with Chichi, he might develop a closer brother - like relationship with Krillin. They could go on adventures together, not having to worry about family responsibilities. Goku could also focus more on mentoring younger fighters, like Gohan, in a more detached way, as a master rather than a father.
Another alternate storyline could be that Goku discovers a new purpose in life. Maybe he gets involved in some sort of inter - galactic peacekeeping mission. Without being tied down by marriage, he could be the first to volunteer for dangerous missions. He might also form an alliance with some of the more powerful and mysterious beings in the universe, which he might not have been able to do if he was married and had family obligations.
The Saiyan race might be affected differently. Gohan might not be born, or if he was, he would be raised in a completely different environment. Without Goku as a father in the traditional sense, Gohan could potentially turn out to be more independent or follow a different path in life, perhaps not even being interested in fighting like his father was.
The story would be quite different. Goku might have more freedom to pursue his battles without having to worry about Chichi's concerns. It could also affect the relationships with his kids and the way he interacts with the other characters.
Maybe in this fanfiction, Goku realizes that he and Chi - Chi have very different personalities. Chi - Chi is often more concerned with family and a stable life, while Goku is a free - spirited adventurer. This clash of values could lead him to decide not to marry her. For example, Chi - Chi may want Goku to stay at home and help raise Gohan, but Goku is eager to explore new planets and fight powerful enemies.
One possible storyline could be that Izuku discovers a different quirk within himself. Maybe a latent quirk that was overshadowed by his admiration for All Might and One for All. For example, he could have a quirk related to intelligence amplification, which would make him a brilliant strategist in hero battles.
One interesting storyline could be Goku and Chichi going on a unique adventure together that tests their relationship in new ways. For example, they might have to face a new enemy that specifically targets their love for each other.
There are also fanfics that focus on Chichi's efforts to keep the family together when Goku is away for long periods due to battles or training. It shows her strength as a mother and a wife, and how she manages the household and raises the kids on her own at times.
One popular storyline could be their adventures together in the mountains. They might encounter strange creatures and have to use their wits and skills to overcome difficulties. For example, they could find a lost magical item and have to return it to its rightful place.
Well, one possible plot could be that Goku is under some sort of mind - control during a fight and accidentally hurts Chichi. Maybe an enemy has found a way to manipulate Goku's actions, and in his trance - like state, he strikes out at Chichi without realizing it.
In a 'chichi and goku married' fanfiction, the plot could revolve around their family growing. They already have Gohan, and perhaps they decide to have more children. There could be cute family moments like Goku trying to understand modern parenting techniques that Chichi is into, and also some action when enemies target their family due to Goku's reputation.
One reason could be ChiChi's overbearing nature. She is often very strict about Goku's training and how he spends his time. In fanfiction, this could be exaggerated to the point where Goku finally gets fed up. For example, if she constantly nags him about not doing enough chores around the house instead of training, it might push Goku to his limit.