Great point, so why doesn't she? Because she's not a superhero out to save the world and neither are her friends.And you can't just disregard Bulma's opinion because she alone could have stopped a still human Gero with her resources.
Notice how he blows up the whole island without regard for anyone's life? Revenge for his defeat may have been his fundamental goal but that never stopped him from killing innocent people. At the 22nd TB, he's JUST starting to change, something that's only clear after the Saiyan arc, but only JUST. He'll kill innocent people if the mood strikes him. That's not conjecture, it's shown. For the sake of not losing the forest from the trees, what this means is Goku is not above sparing someone for a better fight even though he has evidence right in front of him that person will murder people.Notice how when the crowd recognise him as Piccolo he at first seems more irritated than anything and then goes on to give a 2 dimensional villain speech that seems like he's just playing the role
It doens't matter what Vegeta or Piccolo's top priorities are, they are still dangerous. Too dangerous to let live, but he still does so because he likes a challenge.
I don't know what the hell you're arguing anymore. If you think Goku's priority is to save the world, that's a misunderstanding of the nature of the characters and the story. Your statement that the logic of the characters shouldn't be taken so seriously also shows a lack of understanding of the characters and story. It's you brushing aside bad writing, but it's not badly written because it's never been their aim to save the world.
Your view that Goku is so stupid doesn't hold water. When has he EVER been that dumb? And how the hell am I taking this too literally?