Why do Goku and Piccolo learn to drive?

The setup is pure domestic comedy dropped between apocalypses. In Dragon Ball Z episode 125, Goku's Ordeal, first aired in Japan on February 5, 1992, Chi-Chi comes home furious from a grocery run, chased by a wild boar, with no car to show for the Son family's wealth of world saving. Her terms are simple: Goku and Piccolo will get driver's licenses, or they can cook their own meals. Piccolo's protest, that he was not even part of the household, is overruled. Two beings who can fly, teleport, and destroy planets report to driving school.
The episode is anime original: nothing like it happens in Toriyama's manga, where the three years of training before the Androids arrive pass in far fewer pages. It is widely reported and remembered as having grown from Toriyama's own artwork, the chapter cover illustration showing Goku and Piccolo in a car that accompanied the manga around chapters 255 to 256, an image with no scene attached to it. The anime staff, who needed material while the manga's Android arc was still being drawn, built the scene the picture promised. That origin is reported rather than documented in a production record, and this page labels it as such; the episode's date, number, and anime original status are the firm facts.
What the staff built became the most defended filler episode in the franchise. The instructors are a matched pair of disasters, the lessons end in wrecked hovercars and a rescue of a bus full of schoolchildren, and both heroes fail. The running joke outlived the episode: Piccolo's borrowed outfit became a collectible costume in later games, the driving lesson was rebuilt as a mission in Dragon Ball Z: Kakarot in 2020, and Dragon Ball Super: Super Hero still jokes, decades on, that Piccolo never got his license. The manga skipped the three years. The anime spent one of its days at driving school, and it is the day everybody remembers.