Duke knew what Batman was worried about, and he also knew those worries were unnecessary. Duke could guarantee that before Earth even went to war, the Saiyans would arrive first.
Duke had already written the rest of the script. A lineup of Kakarot, Broly, and Vegeta was far too extravagant. If all three appeared together, Earth probably wouldn't be able to handle it. So Broly would appear first, with the excuse that there had been traffic on the way and Kakarot and Vegeta would not arrive until two years later.
After Broly was taken out, Kakarot and Vegeta would descend on Earth together and cause a huge ruckus. If Earth had too many powerful fighters, Kakarot could transform into Super Saiyan 2.
After repeating that three or five times, Kakarot and Vegeta could collect their death payouts with an extra chicken leg, and their sons could make their appearances a few years later. Gohan, Goten, Trunks—every last one of them would show up. By then, there would not only be Ultimate Gohan, but fusion techniques appearing one after another as well.
After that, King Vegeta would lead the Saiyan army to the border. The Galactic Emperor's family, Android Cell, Majin Buu, each would take the stage in turn... If Earth could endure all that, it would be perfect. The war Batman worried about would become even more impossible, because Earth was too small to contain humans capable of conquering the universe!
For the sake of world peace, Duke had worried himself sick. He had accomplished what God could not, so nobody could ask any more of him.
"Your worries are completely unnecessary. Hurry home, wash up, sleep, and play with women! Compared to Tony Stark, you're seriously unprofessional!" After hearing Batman's request, Duke showed him the door.
Batman wanted Duke's