I mean, Goku never's been really all that reactive to danger unless it directly and immediately affects his loved ones in front of him. Hell, he's probably just thinking, "Oh, okay I just need to win this and we'll all be safe." Not to mention living in a universe with Dragonballs probably has made him kind of weird with the idea of everyone dying. It's happened already after all with Majin Buu.
Mostly though, it's probably just the fact that Goku isn't a big thinker. When the exhibition is over, maybe they'll have Bulma slap the shit out of him for being a dumbass and they'll browse over the fact that he may have really screwed things up. But I'm not holding my breathe.