There are no such inappropriate 'Straight Shota' stories in the official Dragon Ball Z canon. Dragon Ball Z mainly focuses on epic battles, power-ups, and the adventures of Goku and his friends to protect the Earth from various villains.
Dragon Ball Z is both anime and manga. The anime was adapted from the manga and they share the same story and characters, but presented in different mediums.
One alternative is to focus on character backstories. You could write about the early days of Piccolo, how he came to be the way he is. Another option is to do crossovers with other non - sexual universes. Maybe a story where the Dragon Ball Z characters meet characters from a magical anime world and they have to work together to solve a problem. Also, you can write about the relationships between the characters in a platonic way, like the deepening of the friendship between Gohan and Krillin.
A Kryptonian in the Dragon Ball Z universe could potentially be a very powerful addition. Their natural abilities like super strength, flight, and heat vision could make them a force to be reckoned with. However, they would also face challenges as the Dragon Ball Z world has its own power scale with ki-based powers. They might have to adapt to the different fighting styles and power sources. Maybe they could learn to use ki in addition to their Kryptonian powers, or they could find a way to combine the two in unique ways.
One interesting crossover could be a battle between Hulk's brute strength and Goku's Super Saiyan power. Maybe in the fanfic, they start off as rivals, with Hulk misunderstanding Goku as a threat to Earth. Their fight would be epic, with Hulk's limitless rage against Goku's increasing power levels. It could also explore how their different universes' power systems interact.
One great Bardock in Dragon Ball Z fanfiction is often depicted as a fearless and noble Saiyan. He is shown as a warrior who, despite the cruel nature of the Saiyan race at that time, had a sense of honor. In some fanfictions, he manages to break free from the control of Frieza in more creative ways than in the original story, making his character even more complex and interesting.
There are indeed popular Dragon Ball Z fanfics. Some fanfics delve into the backstories of secondary characters, like Krillin or Yamcha. By doing this, they give more depth to these characters that might not have had as much focus in the original series. This can make the overall Dragon Ball Z world seem even more rich and diverse.